Erdős Problem 850 to Alternating sum of fourth…
Erdős Problem 850 to Erdős Problem 875
- Erdős Problem 850
- Erdős Problem 851
- Erdős Problem 852
- Erdős Problem 853
- Erdős Problem 854
- Erdős Problem 855
- Erdős Problem 856
- Erdős Problem 858
- Erdős Problem 859
- Erdős Problem 860
- Erdős Problem 862
- Erdős Problem 864
- Erdős Problem 865
- Erdős Problem 867
- Erdős Problem 868
- Erdős Problem 869
- Erdős Problem 871
- Erdős Problem 872
- Erdős Problem 873
- Erdős Problem 875
Erdős Problem 876 to Erdős Problem 930
- Erdős Problem 876
- Erdős Problem 877
- Erdős Problem 878
- Erdős Problem 881
- Erdős Problem 882
- Erdős Problem 883
- Erdős Problem 884
- Erdős Problem 885
- Erdős Problem 886
- Erdős Problem 887
- Erdős Problem 888
- Erdős Problem 889
- Erdős Problem 890
- Erdős Problem 891
- Erdős Problem 894
- Erdős Problem 897
- Erdős Problem 912
- Erdős Problem 913
- Erdős Problem 929
- Erdős Problem 930
Erdős Problem 931 to Erdős Problem 954
- Erdős Problem 931
- Erdős Problem 932
- Erdős Problem 933
- Erdős Problem 935
- Erdős Problem 936
- Erdős Problem 937
- Erdős Problem 938
- Erdős Problem 939
- Erdős Problem 940
- Erdős Problem 942
- Erdős Problem 943
- Erdős Problem 944
- Erdős Problem 945
- Erdős Problem 946
- Erdős Problem 947
- Erdős Problem 948
- Erdős Problem 950
- Erdős Problem 951
- Erdős Problem 952
- Erdős Problem 954
Erdős Problem 955 to Erdős Problem 980
- Erdős Problem 955
- Erdős Problem 961
- Erdős Problem 962
- Erdős Problem 963
- Erdős Problem 964
- Erdős Problem 966
- Erdős Problem 967
- Erdős Problem 968
- Erdős Problem 969
- Erdős Problem 970
- Erdős Problem 971
- Erdős Problem 972
- Erdős Problem 973
- Erdős Problem 974
- Erdős Problem 975
- Erdős Problem 976
- Erdős Problem 977
- Erdős Problem 978
- Erdős Problem 979
- Erdős Problem 980
Erdős Problem 981 to Erdős Problem 1054
- Erdős Problem 981
- Erdős Problem 983
- Erdős Problem 985
- Erdős Problem 987
- Erdős Problem 994
- Erdős Problem 995
- Erdős Problem 997
- Erdős Problem 999
- Erdős Problem 1000
- Erdős Problem 1001
- Erdős Problem 1002
- Erdős Problem 1003
- Erdős Problem 1004
- Erdős Problem 1005
- Erdős Problem 1049
- Erdős Problem 1050
- Erdős Problem 1051
- Erdős Problem 1052
- Erdős Problem 1053
- Erdős Problem 1054
Erdős Problem 1055 to Erdős Problem 1099
- Erdős Problem 1055
- Erdős Problem 1056
- Erdős Problem 1057
- Erdős Problem 1058
- Erdős Problem 1059
- Erdős Problem 1060
- Erdős Problem 1061
- Erdős Problem 1062
- Erdős Problem 1063
- Erdős Problem 1064
- Erdős Problem 1065
- Erdős Problem 1072
- Erdős Problem 1073
- Erdős Problem 1074
- Erdős Problem 1081
- Erdős Problem 1094
- Erdős Problem 1095
- Erdős Problem 1096
- Erdős Problem 1097
- Erdős Problem 1099
Erdős Problem 1100 to Erdős Problem 1146
- Erdős Problem 1100
- Erdős Problem 1101
- Erdős Problem 1102
- Erdős Problem 1106
- Erdős Problem 1107
- Erdős Problem 1108
- Erdős Problem 1109
- Erdős Problem 1110
- Erdős Problem 1113
- Erdős Problem 1122
- Erdős Problem 1134
- Erdős Problem 1135
- Erdős Problem 1136
- Erdős Problem 1137
- Erdős Problem 1138
- Erdős Problem 1139
- Erdős Problem 1140
- Erdős Problem 1141
- Erdős Problem 1142
- Erdős Problem 1146
Erdős Problem 1147 to Erdős Problem 1202
- Erdős Problem 1147
- Erdős Problem 1148
- Erdős Problem 1149
- Erdős Problem 1179
- Erdős Problem 1180
- Erdős Problem 1185
- Erdős Problem 1186
- Erdős Problem 1187
- Erdős Problem 1188
- Erdős Problem 1189
- Erdős Problem 1190
- Erdős Problem 1191
- Erdős Problem 1193
- Erdős Problem 1194
- Erdős Problem 1195
- Erdős Problem 1196
- Erdős Problem 1197
- Erdős Problem 1198
- Erdős Problem 1201
- Erdős Problem 1202
Erdős Problem 1203 to Sum of squares of divisors of…
- Erdős Problem 1203
- Erdős Problem 1204
- Erdős Problem 1205
- Erdős Problem 1206
- Erdős Problem 1209
- Erdős Problem 1210
- Erdős Problem 1211
- Erdős Problem 1212
- Erdős Problem 1213
- Erdős Problem 1214
- Erdős Problem 1217
- Erdős Problem 1221
- Density of ones in the Kolakoski sequence
- The prime numbers
- No powers as partition numbers
- Fractional parts of sums of reciprocals of Catalan numbers \(C(n)\)
- Number of squares \(\bmod n\)
- Euclid-Mullin sequence
- \(a(n) = 2^(2^n)\)
- Sum of squares of divisors of \(n\)
Prime gaps to Least prime \(\ge n\)
- Prime gaps
- Lesser of twin primes
- Ore's harmonic numbers
- Squares of double factorials
- Multiplicative order of 2 mod \(2n+1\)
- Cuban Primes
- Central trinomial coefficients
- Central factorial numbers: \(((2n)!!)^2\)
- Coefficient of \((xyz)^n\) in \(((x+y)(y+z)(z+x))^n\) equaling \(\binom{2n}{n}^3\)
- A binomial coefficient sum
- A binomial coefficient summation
- Primes congruent to \(\{3, 5, 6\} \pmod 7\)
- Least positive multiple of \(n\) in base 10 with digits 0 and 1
- Recamán's sequence
- Practical numbers
- Apéry numbers
- Catalan-Mersenne numbers
- Wolstenholme numbers
- Sum of next \(n\) primes
- Least prime \(\ge n\)
Prime numbers at the beginning… to $a(n) = (\text{smallest prime}…
- Prime numbers at the beginning of the 20th century
- \(a(n)\) is the integer whose decimal digits are the first \(n+1\) decimal digits of \(\pi\)
- Denominator of sum of reciprocals of divisors
- A nonlinear recurrence sequence
- Determinant of Hankel matrix of the first \(2n-1\) prime numbers
- Combinatorial representation of the recurrence \(a(n+2) = 2a(n+1) + 2a(n)\)
- Smallest number \(k\) such that \(kn + 1\) is prime
- Smallest prime \(\equiv 1 \pmod n\)
- Home primes (OEIS A037274)
- Number of primes \(< n^3\)
- Number of primes \(< n^2\)
- Conjectures associated with A038552
- Smallest composite \(c\) such that \(\textrm{primorial}(n) + c\) is prime
- Denominators of coefficients in Stirling's expansion for \(\log(\Gamma(z))\)
- \(a(n) = \sum_{k=1}^n (k^2 \bmod n)\)
- Nearest integer to \(n/\sqrt{2}\)
- Asymptotics of subsets of \(\{1, 2, \dots, n\}\) with integer average
- Maximum exponent in the prime factorization of \(n\)
- Expansion of g.f. \((1-\sqrt{1-4x-4x^2})/(2(1+x))\)
- \(a(n) = (\text{smallest prime} > n^2) - n^2\)
Concatenation of the next \(n\)… to Determinant of matrix with…
- Concatenation of the next \(n\) numbers
- Catalan-Larcombe-French sequence
- Least \(m\) such that \(\phi(m) = n!\)
- Divisibility of \(2^n + 1\) by \(n\)
- Numerator of \(1/\det(M)\) for \(M\[i,j\] = 1/\operatorname{lcm}(i,j)\)
- Number of different products of subsets of \(\{1, 2, \dots, n\}\)
- Reversible multiples \(a(3^n) = 10^{3^{n-2}} - 1\) for powers of \(3\)
- Conjectures associated with A063880
- Numerator - denominator in \(n\)-th harmonic number
- Decimal encoding of the prime factorization of \(n\)
- Conjectures associated with A067720
- Euclid–Fortunate prime coverage
- Sum of \(a(k)/k!\) over divisors equals harmonic number
- Number of times \(n^2 + s^2\) is prime for positive integers \(s < n\)
- Determinant of prime sum indicator matrix
- Number of primes \(p\) such that \(n^n \le p \le n^n + n^2\)
- Number of primes \(p\) such that \(2^n \le p \le 2^n + \mathrm{prime}(n)\)
- Value of \(n\)-th cyclotomic polynomial at \(n\)
- Recurrence \(a(n+2) = |a(n+1)a(n) - a(n)a(n+1)|\) via concatenation
- Determinant of matrix with entries indicating primality of \(i^2 + j^2\)
Alternating sum of signs of… to Conjectures associated with…
- Alternating sum of signs of powers of \(3/2\)
- Smallest factorial containing exactly \(n\) 6's
- Number of times \(n\) occurs as a binary sub-pattern of \(n^2\)
- Smallest \(x\) such that \(\sigma(x) \bmod x = n\)
- Trajectory of 103 under the Reverse and Add! operation in base 3
- \(a(1)=1, a(2)=1, a(n)=(2^{a(n-1)} + 1)/a(n-2)\)
- Smallest \(m > 0\) such that \(n \cdot 2^m + 1\) is prime
- Least \(k > 0\) such that \((k+1)(k+2)\cdots(k+n) + 1\) is prime
- \(a(n) = \sum_{k=0}^n \binom{2k}{k}^3\)
- Number of prime powers strictly between \(n\)-th prime and \((n+1)\)-th prime
- Conjecture relating two characterizations of a set of integers.
- Denominator of \(\sum_{k=1}^n k^{\mu(k)}\)
- Primes of the form 2^n + 2^i + 1
- Smallest palindrome with exactly \(n\) divisors
- Smallest prime \(p\) such that \(p + n\) is an \(n\)-th power
- Smallest \(r\) such that (concatenation of \(n\), \(r\) times) \(\cdot 10 + 1\) is prime
- Binary representation of primes that divide a number, in decimal
- Expansion of \((1 - x)/(1 - 2 x + 3 x^2)\)
- Smallest prime formed by concatenation \(n, n-1, \dots, n-k\)
- Conjectures associated with A087719
Number of pairs of twin primes… to Smallest power with base>1 and…
- Number of pairs of twin primes between \(n^2\) and \((n+1)^2\)
- Primality and primitive root property from divisibility \(n \mid (a(n-1) + 2^{n-2})\)
- Tug of war score between prime gap increases and decreases
- Product of composite numbers in triangular intervals
- \(\gcd(\mathrm{numerator}(H_n), n!)\)
- Recurrence \(a(n) = (a(n-1) + a(n-2)) \pmod n\)
- Coefficients in a simultaneous approximation to two polylogarithms
- Expansion of g.f. \((1+x)(3+x)/(1+6x^2+x^4)\)
- Conjectures associated with A100474
- Prime-th recurrence with reversal at each step
- Pentanacci \(\pi\) sequence
- Conjectures associated with A100800
- Conjectures associated with A101779
- Conjectures associated with A102371
- Floor of sum of \(\{n/k\}\)
- \(a(0) = 1\), \(a(n) = a(n-1)a(n-1) + 2\)
- Number of decompositions of \(2n+1\) into \(2p+q\), where \(p\) and \(q\) are both odd primes
- Fibonacci transform satisfying \(|a(n)| = F(n+1)\)
- \(a(n) = 3a(n-1) + a(n-2) - 3a(n-3)\)
- Smallest power with base>1 and exponent \(n\) without digit 0
$a(n) = [x^{2n}] \left(\frac{1… to Conjectures associated with…
- \(a(n) = \[x^{2n}\] \left(\frac{1 + x}{1 - x}\right)^n\)
- Number of zeros in ternary representation of \(2^n\)
- Array read by upward antidiagonals
- Conjectures associated with A105210
- Indicator sequence for 5 Fibonacci numbers with n digits
- Triangular matchstick numbers in the class of prime numbers
- Imaginary part of \(\prod_{k=0}^n (1 + k \cdot i)\), \(i = \sqrt{-1}\)
- Fibonacci-Collatz sequence
- Sum of squares of nonacci numbers
- Riesel Problem
- \(a(n) = 16n^2 + 1\)
- Digital sum of the Fermat number \(2^{2^n} + 1\)
- A108306: Expansion of \((3x+1)/(1-3x-3x^2)\)
- Numbers \(n\) such that \(\phi(n) = \phi(n + \phi(n))\)
- Numbers \(n\) such that the perfect deficiency of \(n\) is \(\le 10\).
- Numerator of \(\sum_{k=1}^n 2^k/k\).
- Numerator of \(\binom{6n-2}{2n} / \left(2 \binom{4n-1}{2n}\right)\)
- Conjectures associated with A109227
- Conjectures associated with A109671
- Conjectures associated with A109845
Conjectures associated with… to Ascending descending base…
- Conjectures associated with A109905
- Conjectures associated with A109908
- Conjectures associated with A109909
- Number of symbols '*' and '^' to write the canonical prime factorization of n
- \(a(n) = \operatorname{lcm}\{1,2,\dots,n\}/\operatorname{denom}(H(n))\)
- Smallest \(m > 0\) such that there are no primes between \(nm\) and \(n(m+1)\) inclusive.
- Conjectures associated with A110854
- Integer part of \(\mathrm{prime}(n)/\pi(n)\)
- Number of refactorable numbers (A033950) \(\le 10^n\)
- Sequence related to NOR bracketings
- A generalized Stern sequence
- Number of digits of n raised to the power of the sum of the digits of n
- Number of digits of n raised to the power of the digital root of n
- Smallest number \(m\) such that \(2^n - m\) and \(2^n + m\) are primes
- Expansion of g.f. \(-(1 - 48x^2 - 256x^3) / ((1 - 4x)(1 + 4x)(1 + 4x + 16x^2))\)
- Conjectures associated with A113252
- Square odd-indexed terms in the recurrence \(a(n) = 8a(n-1) - 8a(n-2) + 8a(n-3) - a(n-4)\)
- Conjectures associated with A113255
- Ascending descending base exponent transform of squares
- Ascending descending base exponent transform of factorials
Ascending descending base… to Factorial distance to nearest…
- Ascending descending base exponent transform of \(2^n\)
- Number of prime powers \(q<=n\) such that also \(q+2\) is a prime power
- Difference between first odd semiprime \(> 2^n\) and \(2^n\)
- Largest odd divisor of \(a(n-1) + \textrm{prime}(n)\)
- Numerator of \(\zeta(4n)/\zeta(2n)^2\) (with \(a(0)=2\) instead of \(-2\))
- Each term is previous term plus floor of harmonic mean of two previous terms.
- Partial sums of \(\binom{2n}{n}^2\)
- \(a(n)\) = the number of values of \(k <= 10^n\) such that \(\sqrt{k(k+1)(k+2)(k+3)+1}\) is prime
- \(a(n) = \sum_{j=1}^{n} (3^j + (-2)^j)\)
- Determinants of 2 X 2 matrices of non-overlapping blocks of 4 consecutive primes
- Number of primes in \(n\)-th row of triangle \(k^2 - k + p_n\)
- Least \(k\) such that cyclotomic polynomial \(\Phi_k(n)\) is prime
- Sum of Fermat number and Mersenne number minus 1: \(2^{2^n} + 2^n - 1\)
- Least \(k \ge 1\) such that \(2 \cdot n^k - 1\) is prime
- Half-Fibonacci sequence
- Ratio of product of GCDs to product of factorials of floor divisions
- Odious primes minus evil primes among first \(n\) primes
- Recurrence involving LCM: \(a(n) = x(n+1)/x(n) - 2\)
- Number of Abelian cubes of length \(3n\) over an alphabet of size 3
- Factorial distance to nearest square
Collatz step differences to Number of ways to write $n = x…
- Collatz step differences
- Representations as \(p + 2^x + 7 \cdot 2^y\) with \(p \equiv 5 \pmod 6\)
- Representations as \(p + 2^x + 11 \cdot 2^y\) with \(p \equiv 1 \pmod 6\)
- Smallest \(m\) such that \(n^3 + m^3 + 1\) is prime
- Number of ways to express \(n\) as sum of square, pentagonal, and hexagonal numbers
- Rowland-style prime-generating recurrence
- Chua's Euclidean prime sequence
- Smallest index \(k > n\) such that \((p_k+p_{k+1})/(p_n+p_{n+1})\) is an integer \(\ge 2\)
- Denominators of \(\sum_{k=1}^n \frac{1}{k 2^k}\)
- Recurrence with fourth powers of binomial coefficients
- Central binomial sum \(a(n) = \sum_{k=0}^n (-4)^k \binom{n}{k}^2 \binom{n-k}{k}^2\)
- Central binomial sum \(a(n) = \sum_{k=0}^n \binom{n}{k}^2 \binom{n-k}{k}^2 (-16)^k\)
- Difference of digit sums in base 3 and base 2
- Van Eck's sequence (OEIS A181391)
- Sum of fourth powers of Fibonacci-like binomial coefficients
- Product of two consecutive primes modulo the next prime
- Recurrence with bitwise XOR
- Number of odd primes between \(n^2\) and \((n+1)^2\) with \((n/p) = 1\)
- Coefficients of \(\prod_{k>0} (1 - x^k/k!)\)
- Number of ways to write \(n = x + y\) (\(0 < x < y < n\)) with \(6x \pm 1\) and \(6y \pm 1\) prime
Normalized convolution of… to Twin primes of the form $(3^n -…
- Normalized convolution of \(\binom{6k}{3k}\binom{3k}{k}\)
- Primorial squared plus one
- Sequence \(a(n) = n + \lfloor n r / t \rfloor + \lfloor n s / t \rfloor\)
- Linear recurrence \(a(n) = 5a(n-1) - 8a(n-2)\) with \(a(0)=0, a(1)=1\)
- Representations of \(n = p + q + (n \bmod 2)q\) with Jacobi symbol constraints
- Number of distinct sums of distinct proper divisors of \(n\)
- Size of smallest subset of \(\{1, 2, \dots, n\}\) with distinct subset sums
- Denominator of \(B_{n+1}(x) - B_{n+1}\)
- Number of primes of the form \(2^n \pm 2^k \pm 1\) with \(0 \le k < n\)
- Primes of the form \(3^n \pm 3^k \pm 1\)
- Lerch quotients of odd primes
- Position of \(n\)-th partial sum of the harmonic series when jointly ranked with \(\{\log(k+1)\}\)
- Expansion of \(\sum_{n \ge 0} \frac{(3n)!}{n!^3} \frac{x^{2n}}{(1-x)^{3n+1}}\)
- Least integer \(m > 1\) dividing no sum of two distinct primorials up to \(P_n\)
- Integrality and supercongruences of the factorial ratio \(\frac{(6n)! n!}{(3n)! (2n)!^2}\)
- Sequence \(\frac{(8n)! n!}{(4n)! (3n)! (2n)!}\)
- Balanced walks on a 4-dimensional cubic lattice with neighbor steps
- Partial sums of \((-1)^{k - \Omega(k)}\)
- Remainder of \(2^{n+2}\) modulo \(n\)
- Twin primes of the form \((3^n - k) 2^n \pm 1\)
Number of \(0\)'s in the binary… to Alternating sum of fourth…
- Number of \(0\)'s in the binary expansion of \(n^2\)
- Smallest deficient multiplier for non-deficiency
- Number of primes between \(n^3 - n\) and \(n^3\)
- Number of primes between \(n^2\) and \(n^2 + (\log_2 n)^2\)
- Recurrence \(a(n+1) = 2n(n+1)a(n) - n^4 a(n-1)\) and associated polynomials
- Smallest integer \(s > n\) such that \(1 + 2s + 3s^2 + \dots + n s^{n-1}\) is prime
- Partitions \(n = x + y\) with \(x^2 + xy + y^2\) prime
- Partitions \(2n + 1 = x + y\) with \(x^4 + y^4\) prime
- Primes \(p < n\) with \(n^2 - n + p\) and \(n^2 + n - p\) prime
- Representations of \(n\) using prime pairs with prime gaps of \(6\)
- Partitions of \(n\) into \(x + y\) with \((xy)^2 + 1\) prime
- Partitions of \(n\) into \(x + y\) with \((xy)^2 + xy + 1\) prime
- A double sum of five binomial factors
- Trajectory of \(64\) under the map \(n \to \text{A006368}(n)\)
- Existence of integers \(k\) with \(k^2 \operatorname{XOR} (k+1)^2 = (2n+1)^2\)
- Determinant of Legendre symbol matrix with factorial shifts
- Representation of sequence terms by harmonic numbers \(\lfloor \frac{1}{2H(n) - H(n^2+n-1) - \gamma} \rfloor\)
- Representations using Sophie Germain primes and twin prime pairs
- Eighth root of the generating function of an Apéry-like sequence
- Alternating sum of fourth powers of binomial coefficients
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