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%I #8 Aug 21 2020 05:47:16
%S 8,9,2,8,9,4,5,7,1,4,5,1,2,6,6,0,9,0,4,5,7,0,0,9,4,3,0,0,2,2,4,2,7,0,
%T 9,3,3,6,0,5,0,4,0,8,5,9,4,4,5,6,8,4,3,2,6,4,7,4,9,5,6,7,9,0,7,4,3,7,
%U 2,7,3,4,3,8,7,2,7,6,5,6,4,9,4,9,0,6,6,9,6,8,8,7,3,6,9,4,1,7,8,3
%N Decimal expansion of a constant related to Niven's constant.
%D Steven R. Finch, Mathematical Constants, Cambridge University Press, 2003, Section 2.6 Niven's constant, p. 113.
%H Eric Weisstein's MathWorld, <a href="http://mathworld.wolfram.com/NivensConstant.html">Niven's Constant</a>
%F Equals Sum_(p prime) (zeta(p)-1).
%F Equals Sum_{k>=2} Sum_{p prime} 1/k^p. - _Amiram Eldar_, Aug 21 2020
%e 0.89289457145126609045700943002242709336...
%t digits = 100; k0 = 100; dk = 50; $MaxExtraPrecision = 12*digits; z[n_?NumericQ] := Zeta[Prime[n // Floor]]; Clear[s]; s[k_] := s[k] = NSum[z[n] - 1, {n, 1, k}, WorkingPrecision -> digits + 10, NSumTerms -> 10*digits]*(1 + NSum[Zeta[n] - 1, {n, k + 1, Infinity}, WorkingPrecision -> digits + 10]); s[k0] ; s[k = k0 + dk]; While[RealDigits[s[k], 10, digits] != RealDigits[s[k - dk], 10, digits], Print["k = ", k]; k = k + dk]; RealDigits[s[k], 10, digits] // First
%Y Cf. A033150, A072102, A090699.
%K nonn,cons
%O 0,1
%A _Jean-François Alcover_, May 28 2014
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