cp's OEIS Frontend

A087631 Number of n-digit primes ending in 3 in base 10.

%I A087631 #31 Aug 07 2018 11:18:24
%S A087631 1,6,35,268,2092,17263,146565,1274244,11272025,101053126,915743823,
%T A087631 8372470456,77114448042
%N A087631 Number of n-digit primes ending in 3 in base 10.
%F A087631 From _Iain Fox_, Aug 07 2018: (Start)
%F A087631 a(n) ~ (1/4) * Integral_{x=10^(n-1)..10^n} (dx/log(x)).
%F A087631 a(n) = A006879(n) - A087630(n) - A087632(n) - A087633(n), for n > 1.
%F A087631 (End)
%e A087631 a(2) = 6, as there exist 6 two-digit prime numbers (13, 23, 43, 53, 73, and 83) with units place 3.
%e A087631 a(3) = 35, since there are 35 three-digit numbers with units place digit as 3.
%t A087631 Table[Length[Select[Range[10^n + 3, 10^(n + 1) - 7, 10], PrimeQ[#] &]], {n, 5}] (* _Alonso del Arte_, Apr 27 2014 *)
%o A087631 (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 A087631 float r, x;
%o A087631 int c = 0, count = 0;
%o A087631 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 A087631 (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 A087631 Cf. A006879, A073506, A087630, A087632, A087633.
%K A087631 nonn,base,hard,more
%O A087631 1,2
%A A087631 Meenakshi Srikanth (menakan_s(AT)yahoo.com) and _Amarnath Murthy_, Sep 15 2003
%E A087631 More terms from _Ray Chandler_, Oct 04 2003
%E A087631 Offset corrected by _Iain Fox_, Aug 07 2018
%E A087631 a(11) from _Iain Fox_, Aug 07 2018
%E A087631 a(12)-a(13) from _Giovanni Resta_, Aug 07 2018