A342830 Primes p such that A001414(p+q) is the square of a prime, where q is the next prime after p.

11, 73, 461, 659, 787, 977, 1171, 1181, 1571, 1873, 2039, 2267, 3229, 3823, 4159, 5527, 5563, 5651, 5813, 5857, 5881, 6793, 7877, 8117, 8573, 8719, 9133, 9887, 10463, 10867, 11731, 14087, 14533, 15497, 17401, 17881, 17957, 18839, 19181, 19207, 20719, 20981, 21139, 22051, 24979, 26003, 28537

Offset

1,1

Links

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

Example

a(3) = 461 is a term because it is prime, the next prime is 463, and A001414(461+463) = 25 = 5^2 where 5 is prime.

Maple

spf:= proc(n) local t; add(t[1]*t[2], t=ifactors(n)[2]) end proc:
filter:= proc(p) local t; t:= spf(p+nextprime(p));
issqr(t) and isprime(sqrt(t)) end proc:
select(filter, [seq(ithprime(i), i=1..1000)]);

Crossrefs

Cf. A001414.

Sequence in context: A217946 A163775 A092244 * A155634 A335828 A003367

Adjacent sequences: A342827 A342828 A342829 * A342831 A342832 A342833

Keyword

nonn

Author

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

Status

approved