A306930 Primes p of the form 8*k +- 3 such that p-1 has no prime divisor 4*t + 1.

3, 5, 13, 19, 29, 37, 43, 67, 109, 139, 163, 173, 197, 229, 269, 277, 283, 317, 373, 379, 397, 419, 499, 509, 557, 619, 643, 653, 659, 683, 709, 757, 787, 797, 827, 829, 853, 883, 907, 947, 997, 1013, 1117, 1163, 1229, 1237, 1373, 1427, 1453, 1459, 1499

Offset

1,1

References

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.

Links

Amiram Eldar, Table of n, a(n) for n = 1..10000

Maple

with(numtheory); s:=[];
for n from 1 to 1000 do p:=ithprime(n); p2:=((p+16) mod 8);
if (p2=3) or (p2=5) then sw:=1;
   for q in factorset(p-1) do if (q mod 4) = 1 then sw:=-1; break; fi; od:
   if sw=1 then s:=[op(s), p]; fi;
fi;
od:
s;

Mathematica

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

Crossrefs

Cf. A306931, A306932.

Sequence in context: A227031 A157974 A019420 * A019358 A081353 A238092

Adjacent sequences: A306927 A306928 A306929 * A306931 A306932 A306933

Keyword

nonn

Author

N. J. A. Sloane, Mar 16 2019

Status

approved