%I #40 Feb 11 2026 10:59:06

%S 6,8,16,26,28,76,148,159,808,848,916,1143,4036,4959,43239,73432,98716,

%T 144039,146132,226719

%N Numbers k such that F(k) - k is a prime, where F(k) denotes the k-th Fibonacci number.

%e fibonacci(6) - 6 = 8 - 6 = 2 that is a prime;

%e fibonacci(8) - 8 = 21 - 8 = 13 that is a prime.

%p with(combinat): P:=proc(q) local n;

%p for n from 0 to q do

%p if isprime(fibonacci(n)-n) then print(n); fi; od; end: P(10^5);

%t Select[Range[150000],PrimeQ[Fibonacci[#]-#]&] (* _Harvey P. Dale_, May 03 2018 *)

%o (PARI) lista(nn) = {for(n=1, nn, if(ispseudoprime(fibonacci(n)-n), print1(n, ", ")));} \\ _Altug Alkan_, Mar 30 2016

%Y Cf. A000045, A065220, A064269, A069109, A175404.

%K nonn,hard,more

%O 1,1

%A _Paolo P. Lava_, Mar 30 2016

%E a(15)-a(19) from _Giovanni Resta_, Apr 14 2016

%E a(20) from _Michael S. Branicky_, Feb 10 2026