A060515 Integers i > 1 for which there is no prime p such that i is a solution mod p of x^2 = 2.

2, 10, 28, 39, 45, 54, 58, 74, 87, 88, 101, 108, 114, 116, 130, 143, 147, 156, 164, 168, 178, 180, 181, 225, 228, 235, 238, 242, 244, 248, 256, 263, 270, 271, 277, 304, 305, 317, 318, 325, 333, 334, 338, 347, 363, 367, 373, 374, 378, 380, 381, 386, 397, 402

Offset

1,1

Comments

Solutions mod p are represented by integers from 0 to p-1. The following equivalences holds for i > 1: There is a prime p such that i is a solution mod p of x^2 = 2 iff i^2-2 has a prime factor > i; i is a solution mod p of x^2 = 2 iff p is a prime factor of i^2-2 and p > i.

Links

Charles R Greathouse IV, Table of n, a(n) for n = 1..10000

Formula

Integer i > 1 is a term of this sequence iff i^2-2 has no prime factor > i.

Example

a(1) = 2, since there is no prime p such that 2 is a solution mod p of x^2 = 2. a(2) = 10, since there is no prime p such that 10 is a solution mod p of x^2 = 2 and for each integer i from 3 to 9 there is a prime q such that i is a solution mod q of x^2 = 2 (cf. A059772).

Maple

select(t -> max(numtheory:-factorset(t^2-2)) <= t, [$2..1000]); # Robert Israel, Feb 23 2016

Prog

(PARI) is(n)=my(f=factor(n^2-2)[, 1]); n>1&&f[#f]<=n \\ Charles R Greathouse IV, Aug 24 2013

Crossrefs

Cf. A038873, A059772.

Sequence in context: A196648 A220700 A057753 * A109723 A053594 A006331

Adjacent sequences: A060512 A060513 A060514 * A060516 A060517 A060518

Keyword

nonn

Author

Klaus Brockhaus, Mar 24 2001

Status

approved