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%I #23 May 10 2021 05:09:14
%S 14,20,25,27,33,34,35,39,42,43,44,49,50,52,53,54,56,60,61,62,63,64,65,
%T 68,69,72,73,74,75,76,77,81,82,83,85,86,87,88,89,90,91,95,96,97,98,99,
%U 100,101,102,103,104,105,106,107,110,111,112,113,114,115,116,117,118,119,121,122,123,124,125,126,127,128
%N Numbers n such that at least two consecutive elements of the n-th row of A237591 are in increasing order.
%C In other words: numbers n such that the elements of the n-th row of A237591 are not in nonincreasing order.
%C Note that the n-th row of A237591 is also the first half of the associated Dyck path of A237593.
%e 14 is in the sequence because the elements of the 14th row of A237591 are 8, 3, 1, 2, and they are not in nonincreasing order (note that the last two element are in increasing order).
%o (Python)
%o import math
%o from sympy import sqrt
%o def T(n, k): return int(math.ceil((n + 1)/k - (k + 1)/2)) - int(math.ceil((n + 1)/(k + 1) - (k + 2)/2))
%o def isok(n):
%o l = [T(n, k) for k in range(1, int(math.floor((sqrt(8*n + 1) - 1)/2)) + 1)]
%o return any(l[i + 1] > l[i] for i in range(len(l) - 1))
%o print([n for n in range(1, 151) if isok(n)]) # _Indranil Ghosh_, Apr 20 2017
%Y Complement of A285356.
%Y Cf. A196020, A235791, A236104, A237048, A237591, A237593, A245092.
%K nonn
%O 1,1
%A _Omar E. Pol_, Apr 18 2017
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