A357923 a(n) is the least number of terms in the sum S = 1/(n+1) + 1/(n+2) + 1/(n+3) + ... such that S > n.

1, 3, 17, 68, 242, 812, 2619, 8224, 25345, 77006, 231355, 688758, 2034965, 5973932, 17441201, 50678536, 146643235, 422769139, 1214857227, 3480786068, 9946872233, 28357093263, 80667175724, 229020154166, 649028530125, 1836242560272, 5187142333288, 14632132586005

Offset

0,2

Links

Table of n, a(n) for n=0..27.

Formula

From Thomas Scheuerle, Nov 30 2022: (Start)

a(n) ~ ceiling(exp(n + digamma(1+n)) - (1/2) - n).

floor(digamma(a(n)+n+1) - digamma(n+1)) = n. (End)

Example

For n=0, a single term suffices: S = 1/1 > n = 0.
For n=1, a(1) = 3 terms suffice: S = 1/2 + 1/3 + 1/4 > n = 1.
For n=2, a(3) = 17 terms suffice: S = 1/3 + ... + 1/19 > 2.

Crossrefs

Cf. A002387, A358464.

Sequence in context: A061982 A101562 A034566 * A069468 A241776 A270231

Adjacent sequences: A357920 A357921 A357922 * A357924 A357925 A357926

Keyword

nonn

Author

Gil Broussard, Oct 20 2022

Extensions

a(18)-a(27) from Jon E. Schoenfield, Nov 30 2022

Status

approved