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Where the number of terms in simple continued fraction for H(j) exceeds all H(i), j>i and H(k) is the k-th harmonic number.
3

%I #8 Apr 08 2022 07:51:20

%S 1,2,3,5,7,8,9,13,16,17,19,23,25,26,28,29,35,36,43,45,48,49,54,57,62,

%T 72,73,79,88,90,91,99,103,108,110,113,115,116,118,125,128,148,149,157,

%U 163,168,171,172,184,193,199,205,209,234,240,243,259,265,269,270,281,283

%N Where the number of terms in simple continued fraction for H(j) exceeds all H(i), j>i and H(k) is the k-th harmonic number.

%C Where A055573 increases.

%H Amiram Eldar, <a href="/A091532/b091532.txt">Table of n, a(n) for n = 1..4000</a>

%t t = Table[ Length[ ContinuedFraction[ HarmonicNumber[n]]], {n, 1, 299}]; a = {1}; Do[ If[ t[[n]] > t[[a[[ -1]]]], AppendTo[a, n]], {n, 1, 299}]; a

%Y Cf. A001008, A002805, A055573.

%K nonn

%O 1,2

%A _Robert G. Wilson v_, Jan 19 2004