A122869 Primes p that divide Lucas((p-1)/2), where Lucas is A000032.

11, 19, 31, 59, 71, 79, 131, 139, 151, 179, 191, 199, 211, 239, 251, 271, 311, 331, 359, 379, 419, 431, 439, 479, 491, 499, 571, 599, 619, 631, 659, 691, 719, 739, 751, 811, 839, 859, 911, 919, 971, 991, 1019, 1031, 1039, 1051, 1091, 1151, 1171, 1231, 1259

Offset

1,1

Comments

Lucas numbers A000032(n) = Fibonacci(n-1) + Fibonacci(n+1) = A000045(n-1) + A000045(n+1).

Subsequence of A002145, A040105, A064739, A003626, A076518, and A040147.

Final digit of a(n) is 1 or 9.

A002145 is the union of this sequence and A122870, Primes p that divide Lucas((p+1)/2).

Conjecture: This sequence is just the primes congruent to 11 or 19 mod 20. - Charles R Greathouse IV, May 25 2011

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, A122870, A002145, A040105, A053032, A064739, A003626, A076518.

Sequence in context: A357426 A152091 A272550 * A106535 A178150 A214784

Adjacent sequences: A122866 A122867 A122868 * A122870 A122871 A122872

Keyword

nonn

Author

Alexander Adamchuk, Sep 16 2006

Status

approved