A327752 Primes powers (A246655) congruent to 1 mod 5.

11, 16, 31, 41, 61, 71, 81, 101, 121, 131, 151, 181, 191, 211, 241, 251, 256, 271, 281, 311, 331, 361, 401, 421, 431, 461, 491, 521, 541, 571, 601, 631, 641, 661, 691, 701, 751, 761, 811, 821, 841, 881, 911, 941, 961, 971, 991, 1021, 1031, 1051, 1061, 1091, 1151, 1171, 1181, 1201

Offset

1,1

Comments

Numbers k, not powers of 5, such that x^4 + x^3 + x^2 + x + 1 factors into four linear polynomials over GF(k).

This sequence consists of numbers of the form p^e where prime p == 1 (mod 5), p^(2e) where prime p == 4 (mod 5) and p^(4e) where prime p == 2, 3 (mod 5),

Links

Marius A. Burtea, Table of n, a(n) for n = 1..10000

Example

k = 11: in GF(11), x^4 + x^3 + x^2 + x + 1 = (x - 3)*(x - 4)*(x - 5)*(x + 2);
k = 16: let GF(16) = GF(2)[y]/(y^4+y+1), then x^4 + x^3 + x^2 + x + 1 = (x - y^3)*(x - (y^3+y))*(x - (y^3+y^2))*(x - (y^3+y^2+y+1)).

Prog

(PARI) isok(n) = isprimepower(n) && (n%5==1)
(Magma) [n:n in [2..1210]|IsPrimePower(n) and (n mod 5 eq 1)]; // Marius A. Burtea, Sep 26 2019

Crossrefs

Cf. A137827, A327753.

Intersection of A016861 and A246655.

Sequence in context: A110031 A166451 A109307 * A128835 A316171 A184064

Adjacent sequences: A327749 A327750 A327751 * A327753 A327754 A327755

Keyword

nonn

Author

Jianing Song, Sep 24 2019

Status

approved