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A214648 Sum of next a(n) > 1 triangular numbers is a triangular number. 2
2, 5, 125, 51875, 8114028125 (list; graph; refs; listen; history; text; internal format)
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
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
Sequence in context: A270481 A225944 A270588 * A175978 A092922 A093865
KEYWORD
nonn,more
AUTHOR
Alex Ratushnyak, Jul 24 2012
STATUS
approved

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Last modified April 22 17:45 EDT 2024. Contains 371906 sequences. (Running on oeis4.)