%I #21 May 30 2021 14:19:59

%S 2,3,6,11,17,20,25,28,31,32,35,36,42,45,47,55,58,65,67,76,79,86,88,89,

%T 100,102,105,110,111,113,121,122,145,149,166,175,179,193,198,211,218,

%U 223,226,230,240,244,245,256,262,287,292,295,297,298,300

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

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

%C 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

%C 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, ...}.

%H Robert Israel, <a href="/A121617/b121617.txt">Table of n, a(n) for n = 1..10000</a>

%p select(t -> isprime(t^5-(t-1)^5), [$1..1000]); # _Robert Israel_, Jul 10 2018

%t Do[np5=n^5 - (n-1)^5; If[PrimeQ[np5],Print[n]],{n,1,100}]

%t Flatten[Position[Partition[Range[300]^5,2,1],_?(PrimeQ[#[[2]]-#[[1]]]&), 1,Heads-> False]]+1 (* _Harvey P. Dale_, May 30 2021 *)

%o (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

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

%K nonn

%O 1,1

%A _Alexander Adamchuk_, Aug 10 2006