|
%I #8 Feb 23 2023 10:17:57
%S 557,26893,29983,44119,61927,132611,150587,283001,322051,442237,
%T 455033,641239,755317,851057,920761,1234547,1391483,1667147,1885619,
%U 1921657,2167999,2252011,2534953,2984771,3127489,3489841,3745087,3835681,4405547,5955403,5990473,6623117,6833399,7156987,7242337
%N Primes p such that A001414(p^4-1) is the square of a prime.
%H Robert Israel, <a href="/A342825/b342825.txt">Table of n, a(n) for n = 1..400</a>
%e a(3) = 29983 is a term because it is prime and A001414(29983^4-1) = 2*7+3+5+13*2+19+263+521+937+1021 = 2809 = 53^2 and 53 is a prime.
%p spf:= proc(n) local t; add(t[1]*t[2],t=ifactors(n)[2]) end proc:
%p filter:= proc(n) local s; s:= spf(n-1)+spf(n+1)+spf(n^2+1); issqr(s) and isprime(sqrt(s)) end proc:
%p select(filter, [seq(ithprime(i),i=1..10^5)]);
%Y Cf. A001414
%K nonn
%O 1,1
%A _J. M. Bergot_ and _Robert Israel_, Mar 23 2021
|
