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Primes p that divide Lucas((p-1)/2), where Lucas is A000032.
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%I #32 Jun 06 2024 06:26:27

%S 11,19,31,59,71,79,131,139,151,179,191,199,211,239,251,271,311,331,

%T 359,379,419,431,439,479,491,499,571,599,619,631,659,691,719,739,751,

%U 811,839,859,911,919,971,991,1019,1031,1039,1051,1091,1151,1171,1231,1259

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

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

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

%C Conjecture: This sequence is just the primes congruent to 11 or 19 mod 20. - _Charles R Greathouse IV_, May 25 2011

%H Amiram Eldar, <a href="/A122869/b122869.txt">Table of n, a(n) for n = 1..10000</a> (terms 1..1000 from Vincenzo Librandi)

%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/GaussianPrime.html">Gaussian Prime</a>.

%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/LucasNumber.html">Lucas Number</a>.

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

%o (PARI) lista(kmax) = {my(lucas1 = 1, lucas2 = 3, lucas3, p); for(k = 3, kmax, lucas3 = lucas1 + lucas2; p = 2*k + 1; if(isprime(p) && !(lucas3 % p), print1(p, ", ")); lucas1 = lucas2; lucas2 = lucas3);} \\ _Amiram Eldar_, Jun 06 2024

%Y Cf. A000032, A000045, A053032, A076518, A122870.

%Y Subsequence of A002145, A003626, A040105, A040147 and A064739.

%K nonn

%O 1,1

%A _Alexander Adamchuk_, Sep 16 2006