A053027 Odd primes p with 2 zeros in Fibonacci numbers mod p.

3, 7, 23, 41, 43, 47, 67, 83, 103, 107, 127, 163, 167, 223, 227, 241, 263, 281, 283, 307, 347, 367, 383, 401, 409, 443, 449, 463, 467, 487, 503, 523, 547, 563, 569, 587, 601, 607, 641, 643, 647, 683, 727, 743, 769, 787, 823, 827, 863, 881, 883, 887, 907, 929

Offset

1,1

Comments

Also, odd primes that divide Lucas numbers of even index. - T. D. Noe, Jul 25 2003

Primes in A053030. - Jianing Song, Jun 19 2019

Links

T. D. Noe, Table of n, a(n) for n=1..1000

C. Ballot and M. Elia, Rank and period of primes in the Fibonacci sequence; a trichotomy, Fib. Quart., 45 (No. 1, 2007), 56-63 (The sequence B3).

Nicholas Bragman and Eric Rowland, Limiting density of the Fibonacci sequence modulo powers of p, arXiv:2202.00704 [math.NT], 2022.

M. Renault, Fibonacci sequence modulo m

Formula

A prime p = prime(i) is in this sequence if p > 2 and A001602(i)/2 is even. - T. D. Noe, Jul 25 2003

Crossrefs

Cf. A001176, A053030.

Cf. A000204 (Lucas numbers), A001602 (index of the smallest Fibonacci number divisible by prime(n)), A053028 (primes dividing no Lucas number), A053032 (primes dividing Lucas numbers of odd index).

Sequence in context: A213897 A291776 A135570 * A133432 A133433 A029932

Adjacent sequences: A053024 A053025 A053026 * A053028 A053029 A053030

Keyword

nonn

Author

Henry Bottomley, Feb 23 2000

Status

approved