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%I #31 Aug 07 2018 11:18:24
%S 1,6,35,268,2092,17263,146565,1274244,11272025,101053126,915743823,
%T 8372470456,77114448042
%N Number of n-digit primes ending in 3 in base 10.
%F From _Iain Fox_, Aug 07 2018: (Start)
%F a(n) ~ (1/4) * Integral_{x=10^(n-1)..10^n} (dx/log(x)).
%F a(n) = A006879(n) - A087630(n) - A087632(n) - A087633(n), for n > 1.
%F (End)
%e a(2) = 6, as there exist 6 two-digit prime numbers (13, 23, 43, 53, 73, and 83) with units place 3.
%e a(3) = 35, since there are 35 three-digit numbers with units place digit as 3.
%t Table[Length[Select[Range[10^n + 3, 10^(n + 1) - 7, 10], PrimeQ[#] &]], {n, 5}] (* _Alonso del Arte_, Apr 27 2014 *)
%o (Java) /** The terms of the sequences are generated by changing the range for j for the various numbers of digits. E.g., it ranges from 100 to 999 for three-digit numbers. */
%o float r, x;
%o int c = 0, count = 0;
%o for (float j = 100f; j < 1000f; j++) { for (float i = 2f; i < j; i++) { r = j % i; if (r == 0) c = 1; } if (c == 0) { x = j % 10; if (x == 3) count = count + 1; } c = 0; } System.out.println("count = " + count);
%o (PARI) a(n) = my(c=0); forprime(p=10^(n-1), 10^n, if(p%10==3, c++)); c \\ _Iain Fox_, Aug 07 2018
%Y Cf. A006879, A073506, A087630, A087632, A087633.
%K nonn,base,hard,more
%O 1,2
%A Meenakshi Srikanth (menakan_s(AT)yahoo.com) and _Amarnath Murthy_, Sep 15 2003
%E More terms from _Ray Chandler_, Oct 04 2003
%E Offset corrected by _Iain Fox_, Aug 07 2018
%E a(11) from _Iain Fox_, Aug 07 2018
%E a(12)-a(13) from _Giovanni Resta_, Aug 07 2018
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