A091295 (Number of primes == 3 mod 4 less than 10^n) - (number of primes == 1 mod 4 less than 10^n).

1, 2, 7, 10, 25, 147, 218, 446, 551, 5960, 14252, 63337, 118472, 183457, 951700, 3458334, 6284060, 2581691, 80743228, 259753425

Offset: 1

Author

Enoch Haga, Feb 23 2004

Keywords

• nonn
• more

Examples

			a(1) = 1 because below 10^1 3 and 7 are 3 mod 4 and 5 is 1 mod 4 and the difference is 2-1=1.
		

References

• Hans Riesel, Prime Numbers and Computer Methods for Factorization, 2nd ed., Birkhauser, The distribution of primes between the two series 4n+1 and 4n+3, pages 73-77, with graphs.

Links

• Marc Deléglise, Pierre Dusart, and Xavier-Francois Roblot, Counting primes in residue classes, Math. Comp. 73 (2004), no. 247, 1565-1575.
• Carlos Rivera, Puzzle 256, Jack Brennen old records, The Prime Puzzles & Problems Connection.

Crossrefs

Cf. A091098, A091099. A002144, A002145, A091318, A091267.

Formula

a(n) = A091099(n) - A091098(n) = A093153(n) + 1. [Max Alekseyev, May 17 2009]

Extensions

a(17)-a(20) from Marc Deleglise, Jun 28 2007