cp's OEIS Frontend

This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.

A290864 Numbers k such that the k-th Fibonacci polynomial evaluated at k is prime.

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%I A290864 #44 Jun 17 2025 09:22:54
%S A290864 2,5,71,8419
%N A290864 Numbers k such that the k-th Fibonacci polynomial evaluated at k is prime.
%C A290864 Numbers k such that A084844(k) = A117715(k,k) is prime.
%C A290864 a(5) > 9200. - _Giovanni Resta_, Aug 13 2017
%C A290864 Except for a(1), all terms == 1 or 5 (mod 6). - _Robert Israel_, Aug 13 2017
%H A290864 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/FibonacciPolynomial.html">Fibonacci Polynomial</a>
%H A290864 Wikipedia, <a href="https://en.wikipedia.org/wiki/Fibonacci_polynomials">Fibonacci polynomials</a>
%e A290864 5 is in the sequence because A117715(5,5) = 701 is prime.
%p A290864 select(t -> isprime(combinat:-fibonacci(t,t)), [2,seq(seq(6*i+j,j=[1,5]),i=0..100)]); # _Robert Israel_, Aug 13 2017
%t A290864 Select[Range[100], PrimeQ@ Fibonacci[#, #] &] (* _Giovanni Resta_, Aug 13 2017 *)
%Y A290864 Cf. A000045, A011973, A084844, A117715, A162515, A168561.
%K A290864 nonn,more,hard
%O A290864 1,1
%A A290864 _Bobby Jacobs_, Aug 12 2017
%E A290864 a(4) from _Giovanni Resta_, Aug 13 2017