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.

A345231 Decimal expansion of 1/sqrt(Pi) * Product_{p primes} sqrt(p*(p-1)) * log(p/(p-1)).

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%I A345231 #19 Jun 13 2021 05:07:21
%S A345231 5,4,6,8,5,5,9,5,5,2,8,0,4,7,4,4,6,6,8,4,5,5,1,7,1,0,0,9,9,0,7,6,1,7,
%T A345231 8,9,9,1,0,2,1,0,4,8,5,9,2,9,7,4,2,9,4,7,8,2,8,6,8,9,3,7,1,4,9,9,3,5,
%U A345231 1,4,8,6,2,7,3,9,1,5,5,1,7,1,5,2,7,6,8,7,1,6,0,0,2,3,7,8,3,1,0,3,2,8,7,9,8,8
%N A345231 Decimal expansion of 1/sqrt(Pi) * Product_{p primes} sqrt(p*(p-1)) * log(p/(p-1)).
%H A345231 Steven R. Finch, <a href="https://doi.org/10.1017/9781316997741">Mathematical Constants II</a>, Encyclopedia of Mathematics and Its Applications, Cambridge University Press, Cambridge, 2018, p. 50.
%H A345231 Ramanujan's Papers, <a href="https://web.archive.org/web/20200124035942/http://ramanujan.sirinudi.org/Volumes/published/ram17.html">Some formulas in the analytic theory of numbers</a>, Messenger of Mathematics, XLV, 1916, 81-84, Formula (7), constant A1.
%F A345231 Equals lim_{n->infinity} sqrt(log(n))/n * Sum_{k=1..n} 1/d(k), where d(n) = A000005(n).
%F A345231 Equals A083281/sqrt(Pi).
%e A345231 0.5468559552804744668455171009907617899102104859297429478286893714993514862739...
%t A345231 $MaxExtraPrecision = 1000; Clear[f]; f[p_] := Sqrt[p*(p - 1)]*Log[p/(p - 1)]; Do[cc = Rest[CoefficientList[Series[Log[f[1/x]], {x, 0, m}], x, m + 1]]; Print[1/Sqrt[Pi] * f[2] * Exp[N[Sum[Indexed[cc, n] * (PrimeZetaP[n] - 1/2^n), {n, 2, m}], 110]]], {m, 100, 500, 100}]
%Y A345231 Cf. A000005, A083281, A345288.
%K A345231 nonn,cons
%O A345231 0,1
%A A345231 _Vaclav Kotesovec_, Jun 11 2021