A353130 a(n) = floor(H(n) + exp(H(n))*log(H(n))) - n, where H(n) = Sum_{k=1..n} 1/k.

0, 1, 2, 3, 5, 6, 8, 9, 11, 13, 14, 16, 18, 19, 21, 23, 24, 26, 28, 30, 32, 34, 35, 37, 39, 41, 43, 45, 47, 49, 51, 53, 55, 57, 59, 61, 63, 65, 67, 69, 71, 73, 75, 77, 79, 81, 83, 85, 87, 89, 91, 93, 96, 98, 100, 102, 104, 106, 108, 110, 113, 115, 117, 119, 121, 123, 126, 128

Offset: 1

Author

Omar E. Pol, Apr 24 2022

Keywords

• nonn

Comments

About Lagarias's theorem and the Riemann hypothesis the graph of A057640 vs. A000203 is essentially equivalent to the graph of this sequence vs. A001065 (see Plot 2 in the Links section and A057640, A057641).

Links

• J. C. Lagarias, An elementary problem equivalent to the Riemann hypothesis, arXiv:math/0008177 [math.NT], 2000-2001; Am. Math. Monthly 109 (#6, 2002), 534-543.
• OEIS Plot 2, A353130 vs A001065

Crossrefs

Cf. A000203, A057640, A057641, A001065.

Programs

Mathematica

a[n_] := Module[{h = HarmonicNumber[n]}, Floor[h + Exp[h]*Log[h]] - n]; Array[a, 100] (* Amiram Eldar, Apr 26 2022 *)

PARI

H(n) = sum(k=1, n, 1/k)
a(n) = floor(H(n) + exp(H(n))*log(H(n))) - n \\ Felix Fröhlich, Apr 26 2022

Formula

a(n) = A057640(n) - n.

a(n) = A057641(n) + A001065(n).