Sequences

Number of cycles of function f(x) = x^10 mod n.

Numbers k such that F(k) == -1 (mod k), where F(n) = A000045(n) is the n-th Fibonacci number.

Numbers k such that Fibonacci(k) == -2 (mod k).

Numbers k such that Fibonacci(k) == -3 (mod k).

Numbers k such that Fibonacci(k) == -5 (mod k).

Numbers k such that Fibonacci(k) == -8 (mod k).

Numbers k such that Fib(k) == -13 (mod k).

Numbers k such that Fib(k) == -21 (mod k).

Numbers k such that Fib(k) == -34 (mod k).

Numbers k such that Fibonacci(k) == -55 (mod k).

Numbers k such that Fib(k) == -89 (mod k).

Self-Fibonacci numbers: numbers k that divide Fibonacci(k).

Numbers k such that Fibonacci(k) == 1 (mod k).

Numbers k such that Fibonacci(k) == 2 (mod k).

Numbers k such that Fibonacci(k) == 3 (mod k).

Numbers k such that Fibonacci(k) == 5 (mod k).

Numbers k such that Fibonacci(k) == 8 (mod k).

Numbers k such that Fib(k) == 13 (mod k).

Numbers k such that Fib(k) == 21 (mod k).

Numbers k such that Fibonacci(k) == 34 (mod k).

Numbers k such that Fibonacci(k) == 55 (mod k).

Numbers k such that Fibonacci(k) == 89 (mod k).

a(n) = least k such that Fibonacci(k) ends with n, or -1 if there are none.

Least Fibonacci number ending with n.

Square of main diagonal of 3-dimensional box with coprime integer sides and integer face diagonals.

Lonely (or isolated) primes: increasing distance to nearest prime.

Distances of increasingly lonely primes to nearest prime.

Lonely (or isolated) primes: least prime of distance n from nearest prime (n = 1 or even).

Conjecturally, number of infinitely recurring prime patterns of width 2n-1.

Conjecturally, maximum number of primes in an infinitely-recurring prime pattern of width 2*n-1.

Conjecturally, number of maximal infinitely-recurring prime patterns of width 2*n-1.

Conjecturally, number of infinitely-recurring prime patterns on n consecutive integers.

a(n) gives the largest number k for which there is at least one admissible k-tuple taken from [0, 1, ..., n-1] if the tuple starts with 0. Admissibility is defined in a comment.

Numbers whose sum of divisors is prime.

Prime numbers that are the sum of the divisors of some n.

Nondeficient numbers: numbers k such that sigma(k) >= 2k; union of A000396 and A005101.

Numbers k such that sigma(k) >= 3*k.

Numbers k such that sigma(k) >= 4*k.

a(n) is the least k with sigma(k) >= n*k.

Primes p such that p + 4 is also prime.

Primes p such that p + 6 is also prime. (Lesser of a pair of sexy primes.)

Primes p such that p + 8 is also prime.

Primes p such that p + 10 is also prime.

Primes p such that 2*p + 3 is also prime.

Numbers m such that m and 2*m + 5 are both prime.

Numbers m such that m and 2*m + 7 both prime.

Numbers m such that m and 2*m + 9 both prime.

Primes p such that 3*p + 2 is also prime.

Primes p such that 3p + 4 is also prime.

Primes p such that 3*p + 8 is also prime.