A306932 Primes p of the form 8*k + 5 such that every odd prime divisor of p-1 has the form 8*t + 7.

5, 29, 197, 317, 509, 797, 1373, 1949, 2213, 2909, 3557, 3677, 4157, 4229, 4253, 4349, 5309, 5573, 5693, 6173, 6269, 6653, 7517, 7589, 8573, 8837, 9533, 10589, 11069, 11549, 14813, 15749, 15773, 17573, 17669, 17789, 18077, 18269, 19037, 19997, 20357

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 2 to 5000 do
p:=ithprime(n); p2:=((p+16) mod 8);
if (p2=5) then sw:=1;
   for q in factorset(p-1) do if ( (q mod 2)=1) and (q mod 8) <> 7 then sw:=-1; break; fi; od:
   if sw=1 then s:=[op(s), p]; fi;
fi;
od:
s; # A306932

Mathematica

Select[8*Range[0, 2500] + 5, PrimeQ[#] && AllTrue[FactorInteger[# - 1][[;; , 1]], #1 == 2 || Mod[#1, 8] == 7 &] &] (* Amiram Eldar, Dec 05 2020 *)

Crossrefs

Cf. A306930, A306931.

Sequence in context: A095000 A086672 A324962 * A201856 A201115 A199419

Adjacent sequences: A306929 A306930 A306931 * A306933 A306934 A306935

Keyword

nonn

Author

N. J. A. Sloane, Mar 16 2019

Status

approved