A065454 Let the k-th harmonic number be H(k) = Sum_{i=1..k} 1/i = P(k)/Q(k) = A001008(k)/A002805(k); sequence gives values of k such that Q(k) = Q(k+1).

9, 11, 13, 14, 21, 25, 27, 29, 33, 34, 35, 37, 38, 39, 44, 45, 47, 49, 50, 51, 54, 55, 56, 57, 59, 61, 64, 67, 69, 73, 74, 75, 77, 79, 81, 83, 84, 85, 86, 89, 90, 91, 92, 93, 94, 95, 97, 98, 101, 103, 105, 107, 110, 111, 113, 114, 115, 116, 117, 118, 121, 122, 123, 125

Offset: 1

Author

Benoit Cloitre, Nov 24 2001

Keywords

• nonn

Comments

Shiu (2016) proved that this sequence is infinite. Wu and Chen (2019) proved that the asymptotic density of this sequence is 1. - Amiram Eldar, Jan 29 2021

Examples

			For example: H(11) = 83711/27720, H(12) = 86021/27720 and so a(2) = 11.
		

Links

• Amiram Eldar, Table of n, a(n) for n = 1..10000
• Peter Shiu, The denominators of harmonic numbers, arXiv:1607.02863 [math.NT], 2016.
• Bing-Ling Wu and Yong-Gao Chen, On the denominators of harmonic numbers, II, Journal of Number Theory, Vol. 200 (2019), pp. 397-406.

Crossrefs

Cf. A001008, A002805.

Programs

Mathematica

Position[Partition[Denominator @ HarmonicNumber[Range[126]], 2, 1], {x_, x_}] // Flatten (* Amiram Eldar, Jan 29 2021 *)