A242972 - OEIS

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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

(list; constant; graph; refs; listen; history; text; internal format)

OFFSET

0,1

REFERENCES

Steven R. Finch, Mathematical Constants, Cambridge University Press, 2003, Section 2.6 Niven's constant, p. 113.

LINKS

Table of n, a(n) for n=0..99.

Eric Weisstein's MathWorld, Niven's Constant

FORMULA

Equals Sum_(p prime) (zeta(p)-1).

Equals Sum_{k>=2} Sum_{p prime} 1/k^p. - Amiram Eldar, Aug 21 2020

EXAMPLE

0.89289457145126609045700943002242709336...

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

CROSSREFS

Cf. A033150, A072102, A090699.

Sequence in context: A113210 A021116 A201406 * A198142 A336056 A202623

Adjacent sequences: A242969 A242970 A242971 * A242973 A242974 A242975

KEYWORD

nonn,cons

AUTHOR

Jean-François Alcover, May 28 2014

STATUS

approved