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.

A073506 Number of primes == 3 (mod 10) less than 10^n.

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%I A073506 #15 Feb 16 2025 08:32:46
%S A073506 1,7,42,310,2402,19665,166230,1440474,12712499,113765625,1029509448,
%T A073506 9401979904,86516427946
%N A073506 Number of primes == 3 (mod 10) less than 10^n.
%C A073506 Also Pi(n,5,3)
%C A073506 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 A073506 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/ModularPrimeCountingFunction.html">Modular Prime Counting Function</a>
%F A073506 A073505(n) + a(n) + A073507(n) + A073508(n) + 2 = A006880(n).
%e A073506 a(2)=7 because there are 7 primes == 3 (mod 10) less than 10^2. They are 3, 13, 23, 43, 53, 73 and 83.
%t A073506 c = 0; k = 3; Do[While[k < 10^n, If[PrimeQ[k], c++ ]; k += 10]; Print[c], {n, 1, 10}]
%Y A073506 Cf. A006880, A087631, A073505, A073507, A073508, A073509, A073510, A073511, A073512, A073513, A073514, A073515, A073516, A073517.
%K A073506 base,nonn,more
%O A073506 1,2
%A A073506 _Shyam Sunder Gupta_, Aug 14 2002
%E A073506 Edited by _Robert G. Wilson v_, Oct 03 2002
%E A073506 a(10) from _Robert G. Wilson v_, Dec 22 2003
%E A073506 a(11)-a(13) from _Giovanni Resta_, Aug 07 2018