A214648 Sum of next a(n) > 1 triangular numbers is a triangular number.

2, 5, 125, 51875, 8114028125

Offset

1,1

Comments

Two or more triangular numbers in the sum.

Sum of next a(n) oblong numbers is an oblong number: the same sequence.

Links

Table of n, a(n) for n=1..5.

Formula

a(n) is the smallest integer k > 1 such that (4*k^3 + 12*s*k^2 + 4*(3*s^2-1)*k)/3 + 1 is a square, where s = a(1) + a(2) + ... + a(n-1). - Max Alekseyev, Jan 30 2014

Example

(0+1)=1 is a triangular number, so a(1)=2, then (3+6+10+15+21)=55 is a triangular number, so a(2)=5.

Prog

(Python)
from __future__ import division
from gmpy2 import is_square
A214648_list, s, c, d = [], 0, 0, -1
for _ in range(10):
    k = 2
    q = 4*(k*(k*(k+c)+d))//3 + 1
    while not is_square(q):
        k += 1
        q = 4*(k*(k*(k+c)+d))//3 + 1
    A214648_list.append(k)
    s += k
    c, d = 3*s, 3*s**2-1 # Chai Wah Wu, Mar 01 2016

Crossrefs

Cf. A000217, A073684, A214696, A214697.

Sequence in context: A270481 A225944 A270588 * A175978 A092922 A093865

Adjacent sequences: A214645 A214646 A214647 * A214649 A214650 A214651

Keyword

nonn,more

Author

Alex Ratushnyak, Jul 24 2012

Status

approved