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

1,1

Comments

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

Links

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

Example

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.

Prog

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

Crossrefs

Subsequence of A003627.

Sequence in context: A180231 A141172 A285688 * A139833 A260792 A059700

Adjacent sequences: A383234 A383235 A383236 * A383238 A383239 A383240

Keyword

nonn

Author

Jayde S. Massmann, Apr 20 2025

Status

approved