A337920 Numbers k such that d(k) = d(k+1), where d(k) = A058312(k) is the denominator of the k-th alternating harmonic number.

5, 9, 11, 13, 17, 20, 21, 23, 25, 29, 32, 33, 35, 37, 38, 39, 41, 43, 44, 45, 47, 49, 50, 51, 53, 54, 55, 56, 57, 59, 61, 62, 64, 65, 67, 68, 69, 71, 73, 75, 77, 79, 81, 83, 84, 85, 86, 89, 90, 91, 92, 93, 94, 95, 97, 98, 101, 104, 105, 107, 109, 110, 111, 113

Offset

1,1

Comments

The asymptotic density of this sequence is 1 (Wu and Chen, 2019).

Links

Amiram Eldar, Table of n, a(n) for n = 1..10000

Bing-Ling Wu and Yong-Gao Chen, On the denominators of harmonic numbers, II, Journal of Number Theory, Vol. 200 (2019), pp. 397-406.

Example

5 is a term since A058312(5) = A058312(6) = 60.

Mathematica

d[n_] := Denominator @ Sum[(-1)^(k + 1)/k, {k, 1, n}]; Position[Partition[d[Range[120]], 2, 1], {x_, x_}] // Flatten

Crossrefs

Cf. A058312, A065454 (analogous with denominators of harmonic numbers).

Sequence in context: A043766 A063479 A161155 * A314585 A078621 A287521

Adjacent sequences: A337917 A337918 A337919 * A337921 A337922 A337923

Keyword

nonn

Author

Amiram Eldar, Jan 29 2021

Status

approved