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Positive numbers n such that 8*n^2-2*n-1 divides Fibonacci(n).
4

%I #22 Apr 03 2023 10:36:11

%S 27,37,97,577,687,727,777,807,1297,1707,1917,2067,2487,2787,2977,3027,

%T 3037,3067,3277,3367,3417,3507,3837,4047,4257,4377,4447,4567,4717,

%U 5137,5557,5637,5677,5917,5967,6057,6187,6327,7077,7087,7357,7407,7507,7597

%N Positive numbers n such that 8*n^2-2*n-1 divides Fibonacci(n).

%C The prime numbers of this sequence are in A159231.

%H Arkadiusz Wesolowski, <a href="/A159259/b159259.txt">Table of n, a(n) for n = 1..1000</a>

%H Chris Caldwell, The Prime Glossary, <a href="https://t5k.org/glossary/xpage/FibonacciNumber.html">Fibonacci number</a>

%t Select[Range[7597], Mod[Fibonacci[#], 8*#^2 - 2*# - 1] == 0 &] (* _Arkadiusz Wesolowski_, Dec 12 2011 *)

%o (Magma) [n : n in [1..7597] | IsZero(Fibonacci(n) mod (8*n^2-2*n-1))] // _Arkadiusz Wesolowski_, Nov 09 2013

%o (PARI) for(n=1, 7597, if(Mod(fibonacci(n), 8*n^2-2*n-1)==0, print1(n, ", "))); \\ _Arkadiusz Wesolowski_, Nov 09 2013

%Y Cf. A000045, A023172, A159234, A159231, A181890.

%K nonn

%O 1,1

%A _Arkadiusz Wesolowski_, Apr 07 2009