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A214696 Sum of next a(n) > 1 positive triangular numbers is a triangular number. 2
3, 7, 13, 17, 4919, 73789919 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

COMMENTS

Two or more triangular numbers in the sum.

Because an oblong number is twice a triangular number, this sequence also gives: the sum of next a(n) positive oblong numbers is an oblong number.

LINKS

Table of n, a(n) for n=1..6.

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 = 1 + a(1) + a(2) + ... + a(n-1). - Max Alekseyev, Jan 30 2014

EXAMPLE

1+3+6 = 10 is a triangular number, so a(1)=3, then 10+15+21+28+36+45+55 = 210 is a triangular number, seven summands, so a(2)=7.

CROSSREFS

Cf. A000217, A073684, A214648.

Sequence in context: A032437 A076746 A243706 * A291661 A310256 A310257

Adjacent sequences:  A214693 A214694 A214695 * A214697 A214698 A214699

KEYWORD

nonn,more

AUTHOR

Alex Ratushnyak, Jul 26 2012

STATUS

approved

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Last modified April 8 08:54 EDT 2020. Contains 333313 sequences. (Running on oeis4.)