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A160591
Indices of primes congruent to 5 modulo 12.
8
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
OFFSET
1,1
COMMENTS
The asymptotic density of this sequence is 1/4 (by Dirichlet's theorem). - Amiram Eldar, Mar 02 2021
LINKS
FORMULA
a(n) = A000720(A040117(n)).
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:
res; # Robert Israel, Dec 26 2016
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.
Sequence in context: A226723 A029918 A081842 * A297466 A198267 A298786
KEYWORD
nonn
AUTHOR
M. F. Hasler, May 21 2009
STATUS
approved