A121617 Numbers n such that A022521(n-1) = n^5 - (n-1)^5 is prime.

2, 3, 6, 11, 17, 20, 25, 28, 31, 32, 35, 36, 42, 45, 47, 55, 58, 65, 67, 76, 79, 86, 88, 89, 100, 102, 105, 110, 111, 113, 121, 122, 145, 149, 166, 175, 179, 193, 198, 211, 218, 223, 226, 230, 240, 244, 245, 256, 262, 287, 292, 295, 297, 298, 300

Offset: 1

Author

Alexander Adamchuk, Aug 10 2006

Keywords

• nonn

Comments

The elements of A022521 are sometimes called Nexus number of order 5, see there.

The terms should have 1 subtracted, since indices of primes in A022521 are 1, 2, 5, 10, 16, 19, 24, 27, 30, 31, 34, 35, 41, 44, 46, .... - M. F. Hasler, Jan 27 2013

Corresponding Nexus Primes of order 5 (or primes of form (n+1)^5 - n^5 = A022521(n)) are listed in A121616 = {31, 211, 4651, 61051, 371281, 723901, 1803001, 2861461, ...}.

Links

• Robert Israel, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A022521, A121616, A121618, A121619, A121620.

Programs

Maple

select(t -> isprime(t^5-(t-1)^5), [$1..1000]); # Robert Israel, Jul 10 2018

Mathematica

Do[np5=n^5 - (n-1)^5; If[PrimeQ[np5],Print[n]],{n,1,100}]
Flatten[Position[Partition[Range[300]^5,2,1],?(PrimeQ[#[[2]]-#[[1]]]&), 1,Heads-> False]]+1 (* _Harvey P. Dale, May 30 2021 *)

PARI

A121617(n,print_all=0)={for(k=2,9e9, ispseudoprime(k^5-(k-1)^5) & !(print_all & print1(k",")) & !n-- & return(k))} \\ M. F. Hasler, Feb 03 2013