A270839 - OEIS

%I #26 Apr 01 2021 08:23:43

%S 2,3,4,7,9,11,19,23,31,43,59,67,71,79,83,103,127,131,163,167,179,191,

%T 223,227,239,251,271,283,311,359,367,379,383,419,431,439,443,463,467,

%U 479,487,491,499,503,523,547,571,587,599,607,631,643,647,659,683,719,727,739,751,787,823,827,839

%N Integers k such that (A003266(k)/A000045(k-1)) is not divisible by k.

%C A270777 is a subsequence.

%C It appears that this sequence generates prime numbers except 4 and 9. [Verified for the first 500 terms. - _Amiram Eldar_, Apr 01 2021]

%H Amiram Eldar, <a href="/A270839/b270839.txt">Table of n, a(n) for n = 1..500</a>

%e 3 is a term because 1*2 is not divisible by 3.

%e 7 is a term because 1*1*2*3*5*13 is not divisible by 7.

%t Select[Range[2, 840], ! Divisible[Fibonorial@ #/Fibonacci[# - 1], #] &] (* Version 10, or *) Select[Range[2, 840], ! Divisible[Product[Fibonacci@ k, {k, #}]/Fibonacci[# - 1], #] &] (* _Michael De Vlieger_, Mar 24 2016 *)

%o (PARI) t(n) = fibonacci(n) * prod(k=1, n-2, Mod(fibonacci(k), n));

%o for(n=2, 1e3, if(lift(t(n)) != 0, print1(n, ", ")));

%Y Cf. A000045, A000057, A003266, A270777.

%K nonn

%O 1,1

%A _Altug Alkan_, Mar 23 2016

%E Offset corrected by _Amiram Eldar_, Apr 01 2021