cp's OEIS Frontend

A087632 Number of n-digit primes ending in 7 in base 10.

%I A087632 #32 Aug 07 2018 11:22:07
%S A087632 1,5,40,262,2103,17210,146590,1274284,11271819,101051725,915754298,
%T A087632 8372478663,77114370790
%N A087632 Number of n-digit primes ending in 7 in base 10.
%F A087632 From _Iain Fox_, Aug 07 2018: (Start)
%F A087632 a(n) ~ (1/4) * Integral_{x=10^(n-1)..10^n} (dx/log(x)).
%F A087632 a(n) = A006879(n) - A087630(n) - A087631(n) - A087633(n), for n > 1.
%F A087632 (End)
%e A087632 a(2) = 5 as there exist 5 two-digit prime numbers (17, 37, 47, 67, and 97) with units place 7.
%e A087632 a(3) = 40, since there are 40 three-digit numbers with units place digit as 7.
%t A087632 Table[Length[Select[Range[10^n + 7, 10^(n + 1) - 3, 10], PrimeQ[#] &]], {n, 5}] (* _Alonso del Arte_, Apr 27 2014 *)
%o A087632 (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 A087632 float r, x;
%o A087632 int c = 0, count = 0;
%o A087632 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 == 7) count = count + 1; } c = 0; } System.out.println("count = " + count);
%o A087632 (PARI) a(n) = my(c=0); forprime(p=10^(n-1), 10^n, if(p%10==7, c++)); c \\ _Iain Fox_, Aug 07 2018
%Y A087632 Cf. A006879, A073507, A087630, A087631, A087633.
%K A087632 nonn,base,hard,more
%O A087632 1,2
%A A087632 Meenakshi Srikanth (menakan_s(AT)yahoo.com) and _Amarnath Murthy_, Sep 15 2003
%E A087632 More terms from _Ray Chandler_, Oct 04 2003
%E A087632 Offset corrected by _Iain Fox_, Aug 07 2018
%E A087632 a(11) from _Iain Fox_, Aug 07 2018
%E A087632 a(12)-a(13) from _Giovanni Resta_, Aug 07 2018