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a(n) = number of primes <= n that end in 3.
5

%I #17 Jul 11 2017 04:51:54

%S 0,0,1,1,1,1,1,1,1,1,1,1,2,2,2,2,2,2,2,2,2,2,3,3,3,3,3,3,3,3,3,3,3,3,

%T 3,3,3,3,3,3,3,3,4,4,4,4,4,4,4,4,4,4,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,

%U 5,5,5,5,6,6,6,6,6,6,6,6,6,6,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,8,8,8,8,8,8,8,8,8,8,9,9,9,9,9,9,9,9

%N a(n) = number of primes <= n that end in 3.

%C Partial sums of A185706.

%H G. C. Greubel, <a href="/A185712/b185712.txt">Table of n, a(n) for n = 1..5000</a>

%H A. Granville and G. Martin, <a href="http://www.arXiv.org/abs/math.NT/0408319">Prime number races</a>, arXiv:math/0408319 [math.NT], 2004.

%H A. Granville and G. Martin, <a href="http://www.dms.umontreal.ca/~andrew/PDF/PrimeRace.pdf">Prime number races</a>, Amer. Math. Monthly, 113 (No. 1, 2006), 1-33.

%t Accumulate[Table[If[PrimeQ[n] && Mod[n, 10] == 3, 1, 0], {n, 50}]] (* _G. C. Greubel_, Jul 10 2017 *)

%Y Cf. A185705, A185706, A185708, A185709, A185711, A185712, A185714, A185715.

%K base,nonn

%O 1,13

%A _N. J. A. Sloane_, Feb 10 2011