A060515 - OEIS

%I #8 Feb 23 2016 19:25:55

%S 2,10,28,39,45,54,58,74,87,88,101,108,114,116,130,143,147,156,164,168,

%T 178,180,181,225,228,235,238,242,244,248,256,263,270,271,277,304,305,

%U 317,318,325,333,334,338,347,363,367,373,374,378,380,381,386,397,402

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

%C 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.

%H Charles R Greathouse IV, <a href="/A060515/b060515.txt">Table of n, a(n) for n = 1..10000</a>

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

%e 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).

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

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

%Y Cf. A038873, A059772.

%K nonn

%O 1,1

%A _Klaus Brockhaus_, Mar 24 2001