cp's OEIS Frontend

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

%I A327752 #14 Sep 08 2022 08:46:24
%S A327752 11,16,31,41,61,71,81,101,121,131,151,181,191,211,241,251,256,271,281,
%T A327752 311,331,361,401,421,431,461,491,521,541,571,601,631,641,661,691,701,
%U A327752 751,761,811,821,841,881,911,941,961,971,991,1021,1031,1051,1061,1091,1151,1171,1181,1201
%N A327752 Primes powers (A246655) congruent to 1 mod 5.
%C A327752 Numbers k, not powers of 5, such that x^4 + x^3 + x^2 + x + 1 factors into four linear polynomials over GF(k).
%C A327752 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),
%H A327752 Marius A. Burtea, <a href="/A327752/b327752.txt">Table of n, a(n) for n = 1..10000</a>
%e A327752 k = 11: in GF(11), x^4 + x^3 + x^2 + x + 1 = (x - 3)*(x - 4)*(x - 5)*(x + 2);
%e A327752 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)).
%o A327752 (PARI) isok(n) = isprimepower(n) && (n%5==1)
%o A327752 (Magma) [n:n in [2..1210]|IsPrimePower(n) and (n mod 5 eq 1)]; // _Marius A. Burtea_, Sep 26 2019
%Y A327752 Cf. A137827, A327753.
%Y A327752 Intersection of A016861 and A246655.
%K A327752 nonn
%O A327752 1,1
%A A327752 _Jianing Song_, Sep 24 2019