cp's OEIS Frontend

This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.

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

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%I A073505 #17 Feb 16 2025 08:32:46
%S A073505 0,5,40,306,2387,19617,166104,1440298,12711386,113761519,1029517130,
%T A073505 9401960980,86516370000
%N A073505 Number of primes == 1 (mod 10) less than 10^n.
%C A073505 Also Pi(n,5,1)
%C A073505 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.
%H A073505 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/ModularPrimeCountingFunction.html">Modular Prime Counting Function</a>
%F A073505 a(n) + A073506(n) + A073507(n) + A073508(n) + 2 = A006880(n).
%e A073505 a(2) = 5 because there are 5 primes == 1 (mod 10) less than 10^2. They are 11, 31, 41, 61 and 71.
%t A073505 c = 0; k = 1; Do[While[k < 10^n, If[PrimeQ[k], c++ ]; k += 10]; Print[c], {n, 1, 10}]
%Y A073505 Cf. A006880, A087630, A073506, A073507, A073508, A073509, A073510, A073511, A073512, A073513, A073514, A073515, A073516, A073517.
%K A073505 base,nonn,more
%O A073505 1,2
%A A073505 _Shyam Sunder Gupta_, Aug 14 2002
%E A073505 Edited by _Robert G. Wilson v_, Oct 03 2002
%E A073505 a(10) from _Robert G. Wilson v_, Dec 22 2003
%E A073505 a(11)-a(13) from _Giovanni Resta_, Aug 07 2018