A392249 Numbers k such that k-1 is a perfect square and k+1 is prime.

1, 2, 10, 82, 226, 442, 1090, 1522, 2026, 3250, 6562, 9802, 11026, 12322, 13690, 15130, 21610, 29242, 47962, 50626, 56170, 59050, 62002, 65026, 74530, 88210, 91810, 95482, 103042, 119026, 123202, 131770, 136162, 140626, 149770, 173890, 178930, 184042, 194482

Offset

1,2

Links

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

Formula

a(n) = A067201(n)^2+1. - Robert Israel, Jan 04 2026

Example

10 is a term, because the smaller neighbor, 9 = 3^2 and the larger neighbor is 11, prime.

Maple

F:= proc(x) if isprime(x^2+2) then x^2+1 fi end proc:
map(F, [$0..1000]); # Robert Israel, Jan 04 2026

Prog

(PARI) isok(k) = issquare(k-1) && isprime(k+1); \\ Michel Marcus, Jan 05 2026

Crossrefs

Subsequence of A163492.

Cf. A067201.

Sequence in context: A231919 A381832 A174962 * A062396 A218294 A286797

Adjacent sequences: A392246 A392247 A392248 * A392250 A392251 A392252

Keyword

nonn

Author

Andi Fugard, Jan 04 2026

Status

approved