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

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

Author

Omar E. Pol, Apr 18 2017

Keywords

• nonn

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.

Examples

			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).
		

Crossrefs

Complement of A285356.

Cf. A196020, A235791, A236104, A237048, A237591, A237593, A245092.

Programs

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