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A285426 Numbers n such that at least two consecutive elements of the n-th row of A237591 are in increasing order.

%I A285426 #23 May 10 2021 05:09:14
%S A285426 14,20,25,27,33,34,35,39,42,43,44,49,50,52,53,54,56,60,61,62,63,64,65,
%T A285426 68,69,72,73,74,75,76,77,81,82,83,85,86,87,88,89,90,91,95,96,97,98,99,
%U A285426 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 A285426 Numbers n such that at least two consecutive elements of the n-th row of A237591 are in increasing order.
%C A285426 In other words: numbers n such that the elements of the n-th row of A237591 are not in nonincreasing order.
%C A285426 Note that the n-th row of A237591 is also the first half of the associated Dyck path of A237593.
%e A285426 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 A285426 (Python)
%o A285426 import math
%o A285426 from sympy import sqrt
%o A285426 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 A285426 def isok(n):
%o A285426     l = [T(n, k) for k in range(1, int(math.floor((sqrt(8*n + 1) - 1)/2)) + 1)]
%o A285426     return any(l[i + 1] > l[i] for i in range(len(l) - 1))
%o A285426 print([n for n in range(1, 151) if isok(n)]) # _Indranil Ghosh_, Apr 20 2017
%Y A285426 Complement of A285356.
%Y A285426 Cf. A196020, A235791, A236104, A237048, A237591, A237593, A245092.
%K A285426 nonn
%O A285426 1,1
%A A285426 _Omar E. Pol_, Apr 18 2017