A122870 Primes p that divide Lucas[(p+1)/2] = A000032[(p+1)/2].

3, 7, 23, 43, 47, 67, 83, 103, 107, 127, 163, 167, 223, 227, 263, 283, 307, 347, 367, 383, 443, 463, 467, 487, 503, 523, 547, 563, 587, 607, 643, 647, 683, 727, 743, 787, 823, 827, 863, 883, 887, 907, 947, 967, 983, 1063, 1087, 1103, 1123, 1163, 1187, 1223

Offset

1,1

Comments

a(n) is a subset of A002145[n] Primes of form 4n+3, Primes which are also Gaussian primes. A002145[n] is a union of a(n) and A122869[n] Primes p that divide Lucas[(p-1)/2]. Final digit of a(n) is 3 or 7, or Mod[a(n),10] = {3,7}. a(n) = A106865[n+1] Primes of the form 2x^2-2xy+3y^2, with x and y nonnegative, or a(n) are primes congruent to 3,7 modulo 20; Mod[a(n),20] = {3,7}. a(n) is a subset of A003631[n] Primes congruent to {2, 3} mod 5, or primes p that divide Fibonacci(p+1), or Inert rational primes in Q(sqrt 5). a(n) is a subset of A053027[n] Odd primes p with 2 zeros in Fibonacci numbers mod p; or odd primes that divide Lucas numbers of even index. a(n) is a subset of A049098[n] Primes p such that p+1 is divisible by a square.

Is this the same as A216816? - R. J. Mathar, Jul 20 2023

Links

Vincenzo Librandi, Table of n, a(n) for n = 1..1000

Eric Weisstein's World of Mathematics, Lucas Number.

Eric Weisstein's World of Mathematics, Gaussian Prime.

Mathematica

Select[Prime[Range[1000]], IntegerQ[(Fibonacci[(#1+1)/2-1]+Fibonacci[(#1+1)/2+1])/#1]&]

Crossrefs

Cf. A000032, A000045, A122869, A002145, A106865, A053027, A049098, A003631.

Sequence in context: A029932 A084739 A133434 * A216816 A079477 A014426

Adjacent sequences: A122867 A122868 A122869 * A122871 A122872 A122873

Keyword

nonn

Author

Alexander Adamchuk, Sep 16 2006

Status

approved