Sequences

a(n) = 5*a(n-1) - a(n-2), with a(0) = 1 and a(1) = 2.

Numbers k such that the k-th tetrahedral number is the sum of 2 tetrahedral numbers.

Arc-cotangent reducible numbers or non-Størmer numbers: largest prime factor of k^2 + 1 is less than 2*k.

Primes congruent to 1 or 2 modulo 4; or, primes of form x^2 + y^2; or, -1 is a square mod p.

Minimal integer square root of -1 modulo p, where p is the n-th prime of the form 4k+1.

NSW numbers: a(n) = 6*a(n-1) - a(n-2); also a(n)^2 - 2*b(n)^2 = -1 with b(n) = A001653(n+1).

Related to Bernoulli numbers.

Related to Genocchi numbers.

Expansion of (1/theta_4(q)^2 -1)/4 in powers of q.

Order of largest (finite) group with n conjugacy classes.

a(n) = 5*a(n-1) - a(n-2).

Mertens's function: Sum_{k=1..n} mu(k), where mu is the Moebius function A008683.

Reduced totient function psi(n): least k such that x^k == 1 (mod n) for all x prime to n; also known as the Carmichael lambda function (exponent of unit group mod n); also called the universal exponent of n.

((2^m - 1) / p) mod p, where p = prime(n) and m = ord(2,p).

Number of divisors of n == 1 (mod 3) minus number of divisors of n == 2 (mod 3).

Glaisher's J numbers.

Multiplicative order of 2 mod 2n+1.

Primes of the form k^2 - k - 1.

Numbers k such that k^2 - k - 1 is prime.

Periods of reciprocals of integers prime to 10.

Value of y in the solution to p = x^2 + y^2, x <= y, with prime p = A002313(n).

Values of x in the solution to p = x^2 + y^2, x <= y, with prime p = A002313(n).

Numbers x such that p = x^2 + 2y^2, with prime p = A033203(n).

Numbers y such that p = x^2 + 2y^2, with prime p = A033203(n).

Least positive integer x such that prime A038873(n) = x^2 - 2y^2 for some y.

Least positive integer y such that A038873(n) = x^2 - 2y^2 for some x.

Maximal kissing number of n-dimensional laminated lattice.

Weight distribution of [8,4,4] Hamming code.

x such that p = (x^2 + 27*y^2)/4, where p is the n-th prime of the form 3*k+1.

Positive y such that p = (x^2 + 27*y^2)/4 where p is the n-th prime of the form 6*k+1.

Numbers x such that p = x^2 - 5y^2, where p == 0, 1, or 4 (mod 5).

Numbers y such that p = x^2 - 5y^2, where p = 0, 1, or 4 (mod 5).

Least positive integer x such that p = (x^2 - 5*y^2)/4 where p is the n-th odd prime such that 5 is a square mod p.

Least positive integer y such that p = (x^2 - 5*y^2)/4 where p is the n-th odd prime such that 5 is a square mod p.

Numbers x such that p = x^2 + 7y^2, with prime p = A033207(n).

Numbers y such that p = x^2 + 7y^2, with prime p = A033207(n).

Consider all primes of form p = (x^2 + 11y^2 )/4; sequence gives values of x.

Consider all primes of form p = (x^2 + 11y^2 )/4; sequence gives values of y.

Degree of rational Poncelet porism of n-gon.

Take solution to Pellian equation x^2 - n*y^2 = 1 with smallest positive y and x >= 0; sequence gives a(n) = y, or 0 if n is a square. A002350 gives values of x.

Take solution to Pellian equation x^2 - n*y^2 = 1 with smallest positive y and x >= 0; sequence gives a(n) = x, or 1 if n is a square. A002349 gives values of y.

Denominators of convergents to cube root of 2.

Numerators of convergents to cube root of 2.

Denominators of convergents to cube root of 3.

Numerators of convergents to cube root of 3.

Denominators of convergents to cube root of 4.

Numerators of convergents to cube root of 4.

Denominators of convergents to cube root of 5.

Numerators of convergents to cube root of 5.

Denominators of continued fraction convergents to cube root of 6.