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Primes p such that A001414(p^4-1) is the square of a prime.
1

%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