A340767 - OEIS

%I #17 Jun 10 2021 12:22:40

%S 2,3,4,5,6,6,7,8,9,10,10,11,11,12,13,13,14,15,16,16,16,17,18,18,19,19,

%T 19,20,21,22,22,23,24,24,24,24,24,25,26,27,27,28,29,30,31,31,32,32,33,

%U 33,33,34,35,35,35,35,35,36,37,38,38,38,38,39,40,40,41,41,41,42,42

%N Number of primes p <= 6*n + 5 that are congruent to 2 modulo 3.

%H Jianing Song, <a href="/A340767/b340767.txt">Table of n, a(n) for n = 0..10000</a>

%F a(n) = A340764(6*n+5).

%F a(n) = 1 + Sum_{k=0..n+1} A167020(k).

%e There are 14 primes <= 6*16+5 = 101 that are congruent to 2 modulo 3, namely 2, 5, 11, 17, 23, 29, 41, 47, 53, 59, 71, 83, 89, 101, so a(16) = 14.

%o (PARI) a(n) = sum(i=1, 6*n+5, isprime(i) && (i%3==2))

%Y Cf. A003627, A167020, A340764, A172104, A296021, A296020.

%K nonn,easy

%O 0,1

%A _Jianing Song_, Apr 28 2021