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A327752 Primes powers (A246655) congruent to 1 mod 5. 3
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 (list; graph; refs; listen; history; text; internal format)
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

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Last modified August 8 08:38 EDT 2022. Contains 356003 sequences. (Running on oeis4.)