A385495 Most significant nonzero decimal digit of zeta(n)-1, where zeta(n) = Sum_{j >= 1} 1/j^n is the Riemann zeta function.
6, 2, 8, 3, 1, 8, 4, 2, 9, 4, 2, 1, 6, 3, 1, 7, 3, 1, 9, 4, 2, 1, 5, 2, 1, 7, 3, 1, 9, 4, 2, 1, 5, 2, 1, 7, 3, 1, 9, 4, 2, 1, 5, 2, 1, 7, 3, 1, 8, 4, 2, 1, 5, 2, 1, 6, 3, 1, 8, 4, 2, 1, 5, 2, 1, 6, 3, 1, 8, 4, 2, 1, 5, 2, 1, 6, 3, 1, 8, 4, 2, 1, 5, 2, 1, 6, 3
Offset: 2
Examples
For n = 4, a(4) = 8 since the most significant digit of zeta(4)-1 = 0.0823232... is 8 (see A013662).
References
- Henri Cohen, Number Theory, Volume II: Analytic and Modern Tools, GTM Vol. 240, Springer, 2007; see pp. 208-209.
Links
- Henri Cohen, High Precision Computation of Hardy-Littlewood Constants, Preprint, 1998.
- Mathematics Stack Exchange, Is the leading digit of the decimal expansion of the prime zeta function at n equal to the first digit of 5^n, for all integers n >= 10?.
- Eric Weisstein's World of Mathematics, Riemann Zeta Function.
- Wikipedia, Riemann Zeta function.
Programs
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Mathematica
Table[First@Select[First@RealDigits[N[Zeta[n] - 1, 100]], # != 0 &], {n, 2, 100}]
Comments