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A159231 Primes p such that 8*p^2-2*p-1 divides Fibonacci(p).

%I A159231 #30 Sep 22 2024 17:47:10
%S A159231 37,97,577,727,1297,3037,3067,4447,4567,5557,7507,7867,8647,9067,9157,
%T A159231 12967,17257,20107,20407,21787,22147,23677,25447,27817,28687,29347,
%U A159231 30187,32587,33487,35617,38377,42157,42667,42967,43207,45697,46447,47497,49477
%N A159231 Primes p such that 8*p^2-2*p-1 divides Fibonacci(p).
%H A159231 Arkadiusz Wesolowski, <a href="/A159231/b159231.txt">Table of n, a(n) for n = 1..1000</a>
%H A159231 Chris Caldwell, The Prime Glossary, <a href="https://t5k.org/glossary/xpage/FibonacciNumber.html">Fibonacci number</a>
%H A159231 C. K. Caldwell, "Top Twenty" page, <a href="https://t5k.org/top20/page.php?id=64">Fibonacci cofactor</a>
%t A159231 Select[Prime@Range[5084], Mod[Fibonacci[#], 8*#^2 - 2*# - 1] == 0 &] (* _Arkadiusz Wesolowski_, Dec 12 2011 *)
%o A159231 (Magma) [p : p in PrimesUpTo(49477) | IsZero(Fibonacci(p) mod (8*p^2-2*p-1))]; // _Arkadiusz Wesolowski_, Nov 09 2013
%o A159231 (PARI) forprime(p=2, 49477, if(Mod(fibonacci(p), 8*p^2-2*p-1)==0, print1(p, ", "))); \\ _Arkadiusz Wesolowski_, Nov 09 2013
%Y A159231 Subsequence of A159259. Supersequence of A215158.
%Y A159231 Cf. A000045, A023172, A159234, A181890.
%K A159231 nonn
%O A159231 1,1
%A A159231 _Arkadiusz Wesolowski_, Apr 06 2009