A270532 Integers k such that A003266(p) is not divisible by p*(p+1)/2 where p is the k-th prime.

1, 2, 4, 9, 14, 19, 23, 27, 31, 38, 39, 48, 49, 61, 73, 76, 86, 90, 91, 93, 96, 99, 101, 107, 111, 117, 118, 124, 129, 138, 143, 144, 150, 153, 154, 155, 161, 166, 179, 188, 192, 195, 208, 213, 217, 219, 224, 229, 236, 243, 247, 250, 253, 258, 261, 262, 269, 272, 276, 277, 283, 285, 292, 300

Offset: 1

Author

Altug Alkan, Mar 18 2016

Keywords

• nonn

Comments

See A000057 to corresponding prime numbers. In other words, this sequence is an indirect way to generate primes dividing all Fibonacci sequences.

Links

• Michel Marcus, Table of n, a(n) for n = 1..1000

Crossrefs

Cf. A000057, A003266, A270475.

Programs

PARI

f(n) = prod(k=1, n, fibonacci(k)); \\ A003266
isok(n) = (lift(Mod(f(prime(n)),(prime(n)*(prime(n)+1)/2))) != 0);

PARI

isok(n) = my(p=prime(n), m=p*(p+1)/2); prod(k=1, p, Mod(fibonacci(k), m)); \\ Michel Marcus, May 14 2021