A073508 Number of primes == 9 (mod 10) less than 10^n.

0, 5, 38, 303, 2390, 19593, 166032, 1440186, 12711333, 113761326, 1029509896, 9401974132, 86516371101

Offset: 1

Author

Shyam Sunder Gupta, Aug 14 2002

Keywords

• base
• nonn
• more

Comments

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 == 9 (mod 10) less than 10^2. They are 19, 29, 59, 79 and 89.
		

Links

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

Crossrefs

Cf. A006880, A087633, A073505, A073506, A073507, A073509, A073510, A073511, A073512, A073513, A073514, A073515, A073516, A073517.

Programs

Mathematica

c = 0; k = 9; Do[While[k < 10^n, If[PrimeQ[k], c++ ]; k += 10]; Print[c], {n, 1, 10}]

Formula

A073505(n) + A073506(n) + A073507(n) + a(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