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

1,1

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.

Links

Table of n, a(n) for n=1..72.

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

Complement of A285356.

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

Sequence in context: A087678 A144585 A186193 * A108874 A063848 A110968

Adjacent sequences: A285423 A285424 A285425 * A285427 A285428 A285429

Keyword

nonn

Author

Omar E. Pol, Apr 18 2017

Status

approved