A342825 Primes p such that A001414(p^4-1) is the square of a prime.

557, 26893, 29983, 44119, 61927, 132611, 150587, 283001, 322051, 442237, 455033, 641239, 755317, 851057, 920761, 1234547, 1391483, 1667147, 1885619, 1921657, 2167999, 2252011, 2534953, 2984771, 3127489, 3489841, 3745087, 3835681, 4405547, 5955403, 5990473, 6623117, 6833399, 7156987, 7242337

Offset

1,1

Links

Robert Israel, Table of n, a(n) for n = 1..400

Example

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.

Maple

spf:= proc(n) local t; add(t[1]*t[2], t=ifactors(n)[2]) end proc:
filter:= proc(n) local s;  s:= spf(n-1)+spf(n+1)+spf(n^2+1); issqr(s) and isprime(sqrt(s)) end proc:
select(filter, [seq(ithprime(i), i=1..10^5)]);

Crossrefs

Cf. A001414

Sequence in context: A260066 A105979 A183779 * A340712 A071393 A352350

Adjacent sequences: A342822 A342823 A342824 * A342826 A342827 A342828

Keyword

nonn

Author

J. M. Bergot and Robert Israel, Mar 23 2021

Status

approved