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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.
1
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
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
KEYWORD
nonn
AUTHOR
Amiram Eldar, Jan 29 2021
STATUS
approved