A383237 Primes p such that x^5+x+1 has no roots modulo p.

2, 29, 41, 47, 71, 131, 179, 197, 233, 239, 257, 269, 311, 353, 443, 461, 491, 509, 587, 647, 653, 683, 761, 857, 863, 887, 929, 947, 1013, 1061, 1223, 1277, 1283, 1289, 1301, 1361, 1373, 1409, 1427, 1439, 1499, 1511, 1559, 1619, 1637, 1733, 1823, 1973, 1979

Offset: 1

Author

Jayde S. Massmann, Apr 20 2025

Keywords

• nonn

Comments

Every term is congruent to 2 modulo 3, hence, except for a(1) = 2, to 5 modulo 6.

Examples

			a(1) = 2 because 0^5+0+1 = 1 and 1^5+1+1 = 3; neither is 0 mod 2.
a(2) = 29, as for p = 3, 5, 7, 11, 13, 17, 19, 23, x^5+x+1 has a root modulo p, namely 1, 2, 2, 9, 3, 10, 3, 15, respectively.
		

Links

• Jayde S. Massmann, Table of n, a(n) for n = 1..1000

Crossrefs

Subsequence of A003627.

Programs

PARI

isok(p) = if (isprime(p), !#polrootsmod(x^5+x+1, p)); \\ Michel Marcus, Apr 20 2025