A242972 Decimal expansion of a constant related to Niven's constant.
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, 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, 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
Offset: 0
Examples
0.89289457145126609045700943002242709336...
References
- Steven R. Finch, Mathematical Constants, Cambridge University Press, 2003, Section 2.6 Niven's constant, p. 113.
Links
- Eric Weisstein's MathWorld, Niven's Constant
Programs
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Mathematica
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
Formula
Equals Sum_(p prime) (zeta(p)-1).
Equals Sum_{k>=2} Sum_{p prime} 1/k^p. - Amiram Eldar, Aug 21 2020