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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.
1
14, 20, 25, 27, 33, 34, 35, 39, 42, 43, 44, 49, 50, 52, 53, 54, 56, 60, 61, 62, 63, 64, 65, 68, 69, 72, 73, 74, 75, 76, 77, 81, 82, 83, 85, 86, 87, 88, 89, 90, 91, 95, 96, 97, 98, 99, 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
OFFSET
1,1
COMMENTS
In other words: numbers n such that the elements of the n-th row of A237591 are not in nonincreasing order.
Note that the n-th row of A237591 is also the first half of the associated Dyck path of A237593.
EXAMPLE
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).
PROG
(Python)
import math
from sympy import sqrt
def T(n, k): return int(math.ceil((n + 1)/k - (k + 1)/2)) - int(math.ceil((n + 1)/(k + 1) - (k + 2)/2))
def isok(n):
l = [T(n, k) for k in range(1, int(math.floor((sqrt(8*n + 1) - 1)/2)) + 1)]
return any(l[i + 1] > l[i] for i in range(len(l) - 1))
print([n for n in range(1, 151) if isok(n)]) # Indranil Ghosh, Apr 20 2017
CROSSREFS
KEYWORD
nonn
AUTHOR
Omar E. Pol, Apr 18 2017
STATUS
approved