A306930 - OEIS

%I #15 Dec 05 2020 03:30:59

%S 3,5,13,19,29,37,43,67,109,139,163,173,197,229,269,277,283,317,373,

%T 379,397,419,499,509,557,619,643,653,659,683,709,757,787,797,827,829,

%U 853,883,907,947,997,1013,1117,1163,1229,1237,1373,1427,1453,1459,1499

%N Primes p of the form 8*k +- 3 such that p-1 has no prime divisor 4*t + 1.

%D L. E. Dickson, History of the Theory of Numbers. Carnegie Institute Public. 256, Washington, DC, Vol. 1, 1919; Vol. 2, 1920; Vol. 3, 1923, see vol. 2, p. 476.

%H Amiram Eldar, <a href="/A306930/b306930.txt">Table of n, a(n) for n = 1..10000</a>

%p with(numtheory); s:=[];

%p for n from 1 to 1000 do p:=ithprime(n); p2:=((p+16) mod 8);

%p if (p2=3) or (p2=5) then sw:=1;

%p    for q in factorset(p-1) do if (q mod 4) = 1 then sw:=-1; break; fi; od:

%p    if sw=1 then s:=[op(s),p]; fi;

%p fi;

%p od:

%p s;

%t Select[Range[1500], MemberQ[{3, 5}, Mod[#, 8]] && PrimeQ[#] && AllTrue[FactorInteger[# - 1][[;; , 1]], Mod[#1, 4] != 1 &] &] (* _Amiram Eldar_, Dec 05 2020 *)

%Y Cf. A306931, A306932.

%K nonn

%O 1,1

%A _N. J. A. Sloane_, Mar 16 2019