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Residues modulo 10 of the irregular primes (A000928).
1

%I #13 Jul 02 2024 07:18:46

%S 7,9,7,1,3,1,9,7,3,7,3,1,3,3,7,1,7,3,9,9,1,9,1,3,1,3,7,1,3,1,7,7,7,7,

%T 3,7,3,7,9,1,7,3,9,3,7,3,1,7,1,7,1,3,7,9,1,1,7,9,7,1,7,9,3,1,1,1,7,9,

%U 1,3,3,1,7,9,7,9,3,1,7,1,7,9,7,7,1,9,9,9,3,9,3,9,7,9,3,9,1,7,3,9,1,3,3,9,7

%N Residues modulo 10 of the irregular primes (A000928).

%D Z. I. Borevich and I. R. Shafarevich, Number Theory. Academic Press, NY, 1966, pp. 425-430 (but there are errors).

%H Amiram Eldar, <a href="/A100639/b100639.txt">Table of n, a(n) for n = 1..10000</a>

%F a(n) = A010879(A000928(n)). - _Amiram Eldar_, Jul 02 2024

%e a(6) = 1 because the 6th irregular prime is 131 and 131 mod 10 = 1.

%t fQ[n_] := Block[{p = n, k = 1}, While[ 2*k <= p - 3 && Mod[ Numerator[ BernoulliB[ 2*k ]], p ] != 0, k++ ]; 2k != p - 1]; Mod[ Select[ Prime[ Range[2, 275]], fQ[ # ] &], 10] (* _Robert G. Wilson v_, Dec 10 2004 *)

%Y Cf. A000928, A010879.

%K easy,nonn

%O 1,1

%A _Pahikkala Jussi_, Dec 04 2004

%E More terms from _Robert G. Wilson v_, Dec 10 2004