A306931 Primes p of the form 8*k + 3 such that every prime divisor of p-2 has the form 8*t + 7.

163, 331, 499, 1171, 1459, 2179, 2203, 2371, 2683, 3019, 5179, 5923, 6043, 6211, 6379, 6883, 7219, 7411, 7723, 8059, 8443, 8563, 9643, 10099, 10651, 10723, 11083, 11131, 11251, 12739, 12763, 13099, 13963, 14779, 14851, 15091, 15451, 16963, 17203

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 3 to 5000 do
p:=ithprime(n); p2:=((p+16) mod 8);
if (p2=3) then sw:=1;
   for q in factorset(p-2) do if (q mod 8) <> 7 then sw:=-1; break; fi; od:
   if sw=1 then s:=[op(s), p]; fi;
fi;
od:
s; # A306931

Mathematica

Select[8*Range[0, 2500] + 3, PrimeQ[#] && AllTrue[FactorInteger[# - 2][[;; , 1]], Mod[#1, 8] == 7 &] &] (* Amiram Eldar, Dec 05 2020 *)

Crossrefs

Cf. A306930, A306932.

Sequence in context: A142772 A212398 A157952 * A142427 A142237 A142283

Adjacent sequences: A306928 A306929 A306930 * A306932 A306933 A306934

Keyword

nonn

Author

N. J. A. Sloane, Mar 16 2019

Status

approved