A160591 - OEIS (original) (raw)

3, 7, 10, 13, 16, 24, 26, 30, 33, 35, 40, 45, 51, 55, 57, 60, 62, 66, 71, 77, 79, 87, 89, 97, 98, 102, 104, 108, 113, 116, 119, 123, 126, 135, 137, 139, 140, 142, 148, 152, 158, 160, 162, 165, 170, 176, 178, 184, 186, 194, 196, 199, 201, 206, 209, 212, 218, 220, 223

COMMENTS

The asymptotic density of this sequence is 1/4 (by Dirichlet's theorem). - Amiram Eldar, Mar 02 2021

EXAMPLE

a(1) = 3 since the 3rd prime, A000040(3) = 5, is the first one to be equal to 5 (mod 12).

a(2) = 7 since the 7th prime, A000040(7) = 17, is the second one to be equal to 5 (mod 12).

MAPLE

res:= NULL: p:= 2:

for m from 2 to 1000 do

p:= nextprime(p);

if p mod 12 = 5 then res:= res, m fi;

od:

MATHEMATICA

Select[{#, Prime[#]}& /@ Range[500], Mod[#[[2]], 12] == 5&] [[All, 1]] (* Jean-François Alcover, Mar 23 2019 *)

Select[Range[300], Mod[Prime[#], 12]==5&] (* Harvey P. Dale, Mar 18 2023 *)

PROG

(PARI) for(n=1, 999, prime(n)%12==5 & print1(n", "))

CROSSREFS

A116602 lists the even terms of this sequence, divided by 2.