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
Keywords
Examples
5 is a term since A058312(5) = A058312(6) = 60.
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.
Programs
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Mathematica
d[n_] := Denominator @ Sum[(-1)^(k + 1)/k, {k, 1, n}]; Position[Partition[d[Range[120]], 2, 1], {x_, x_}] // Flatten
Comments