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

1, 6, 35, 268, 2092, 17263, 146565, 1274244, 11272025, 101053126, 915743823, 8372470456, 77114448042

Offset

1,2

Links

Table of n, a(n) for n=1..13.

Formula

From Iain Fox, Aug 07 2018: (Start)

a(n) ~ (1/4) * Integral_{x=10^(n-1)..10^n} (dx/log(x)).

a(n) = A006879(n) - A087630(n) - A087632(n) - A087633(n), for n > 1.

(End)

Example

a(2) = 6, as there exist 6 two-digit prime numbers (13, 23, 43, 53, 73, and 83) with units place 3.
a(3) = 35, since there are 35 three-digit numbers with units place digit as 3.

Mathematica

Table[Length[Select[Range[10^n + 3, 10^(n + 1) - 7, 10], PrimeQ[#] &]], {n, 5}] (* Alonso del Arte, Apr 27 2014 *)

Prog

(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. */
float r, x;
int c = 0, count = 0;
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);
(PARI) a(n) = my(c=0); forprime(p=10^(n-1), 10^n, if(p%10==3, c++)); c \\ Iain Fox, Aug 07 2018

Crossrefs

Cf. A006879, A073506, A087630, A087632, A087633.

Sequence in context: A244267 A187443 A325115 * A167579 A357095 A030446

Adjacent sequences: A087628 A087629 A087630 * A087632 A087633 A087634

Keyword

nonn,base,hard,more

Author

Meenakshi Srikanth (menakan_s(AT)yahoo.com) and Amarnath Murthy, Sep 15 2003

Extensions

More terms from Ray Chandler, Oct 04 2003

Offset corrected by Iain Fox, Aug 07 2018

a(11) from Iain Fox, Aug 07 2018

a(12)-a(13) from Giovanni Resta, Aug 07 2018

Status

approved