A060591 Integers i > 1 for which there is no prime p such that i is a solution mod p of x^3 = 2.

113, 128, 194, 283, 333, 338, 376, 403, 430, 450, 491, 503, 548, 578, 722, 866, 875, 906, 1008, 1102, 1243, 1244, 1256, 1260, 1365, 1368, 1371, 1392, 1453, 1478, 1529, 1537, 1675, 1718, 1802, 1805, 1911, 1926, 1971, 2051, 2084, 2108, 2132, 2153, 2163

Offset: 1

Author

Klaus Brockhaus, Apr 06 2001

Keywords

• nonn

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^3 = 2 iff i^3-2 has a prime factor > i; i is a solution mod p of x^3 = 2 iff p is a prime factor of i^3-2 and p > i.

Examples

			a(1) = 113, since there is no prime p such that 113 is a solution mod p of x^3 = 2 and for each integer i from 2 to 112 there is a prime q such that i is a solution mod q of x^3 = 2 (cf. A059940).
		

Links

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

Crossrefs

Cf. A040028, A059940.

Programs

Maple

filter:= proc(i) max(numtheory:-factorset(i^3-2)) <= i end proc:
select(filter, [$2..10000]); # Robert Israel, Apr 26 2024

Formula

Integer i > 1 is a term of this sequence iff i^3-2 has no prime factor > i.