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%I #9 Apr 09 2022 01:28:52
%S 1,2,5,12,13,50,61,68,198,1090,1812,2362,32334,1517757,4150055,
%T 8850618,10459960,34693154,80385407,277184250,316848842,426258508,
%U 2150821469,2901738400,49091889811,331178405563
%N Record values of A070266.
%C The corresponding indices are in A353243.
%F a(n) = A070266(A353243(n)).
%t Union @ FoldList[Max, Table[Max[ContinuedFraction[HarmonicNumber[n]]], {n, 1, 10^4}]]
%o (Python)
%o from itertools import count, islice
%o from fractions import Fraction
%o from sympy.ntheory.continued_fraction import continued_fraction
%o def A353244_gen(): # generator of terms
%o k, c = Fraction(), 0
%o for n in count(1):
%o k += Fraction(1,n)
%o if c < (m := max(continued_fraction(k))):
%o yield (c := m)
%o A353244_list = list(islice(A353244_gen(),10)) # _Chai Wah Wu_, Apr 08 2022
%Y Cf. A001008, A002805, A070266, A091532, A353243.
%K nonn,more
%O 1,2
%A _Amiram Eldar_, Apr 08 2022