cp's OEIS Frontend

This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.

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

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%I A214648 #21 Feb 01 2023 17:37:34
%S A214648 2,5,125,51875,8114028125
%N A214648 Sum of next a(n) > 1 triangular numbers is a triangular number.
%C A214648 Two or more triangular numbers in the sum.
%C A214648 Sum of next a(n) oblong numbers is an oblong number: the same sequence.
%F A214648 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
%e A214648 (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.
%o A214648 (Python)
%o A214648 from __future__ import division
%o A214648 from gmpy2 import is_square
%o A214648 A214648_list, s, c, d = [], 0, 0, -1
%o A214648 for _ in range(10):
%o A214648     k = 2
%o A214648     q = 4*(k*(k*(k+c)+d))//3 + 1
%o A214648     while not is_square(q):
%o A214648         k += 1
%o A214648         q = 4*(k*(k*(k+c)+d))//3 + 1
%o A214648     A214648_list.append(k)
%o A214648     s += k
%o A214648     c, d = 3*s, 3*s**2-1 # _Chai Wah Wu_, Mar 01 2016
%Y A214648 Cf. A000217, A073684, A214696, A214697.
%K A214648 nonn,more
%O A214648 1,1
%A A214648 _Alex Ratushnyak_, Jul 24 2012