A073505 Number of primes == 1 (mod 10) less than 10^n.

0, 5, 40, 306, 2387, 19617, 166104, 1440298, 12711386, 113761519, 1029517130, 9401960980, 86516370000

Offset: 1

Author

Shyam Sunder Gupta, Aug 14 2002

Keywords

• base
• nonn
• more

Comments

Also Pi(n,5,1)

This and the related sequences A073505-A073517 and A006880, A073548-A073565 are included because there is interest in the distribution of primes by their initial or final digits.

Examples

			a(2) = 5 because there are 5 primes == 1 (mod 10) less than 10^2. They are 11, 31, 41, 61 and 71.
		

Links

• Eric Weisstein's World of Mathematics, Modular Prime Counting Function

Crossrefs

Cf. A006880, A087630, A073506, A073507, A073508, A073509, A073510, A073511, A073512, A073513, A073514, A073515, A073516, A073517.

Programs

Mathematica

c = 0; k = 1; Do[While[k < 10^n, If[PrimeQ[k], c++ ]; k += 10]; Print[c], {n, 1, 10}]

Formula

a(n) + A073506(n) + A073507(n) + A073508(n) + 2 = A006880(n).

Extensions

Edited by Robert G. Wilson v, Oct 03 2002

a(10) from Robert G. Wilson v, Dec 22 2003

a(11)-a(13) from Giovanni Resta, Aug 07 2018