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Numbers whose square can be written as sum of at least 3 consecutive triangular numbers in two ways.
0

%I #24 Apr 21 2024 11:38:52

%S 286,826,2739,3971,5698,9196,10166,10697,22990,61006,132795,416790,

%T 766480,809380,2396870,2904434,3459006,3688802,4518514,11725659,

%U 13111098,13998608,15709122,22173027,22365267,23636272,23823988,32186742,33630662,33658710,39502086,46387924,59101625,62381858,89841192

%N Numbers whose square can be written as sum of at least 3 consecutive triangular numbers in two ways.

%C Apparently there is an infinity of such numbers and there are no cases of 3 ways.

%e 4518514^2 = T(18801)+..+T(50546) = T(52361)+..+T(64316), where T(n) = A000217(n).

%Y Cf. A000217 (triangular numbers), A257274.

%K nonn

%O 1,1

%A _Zak Seidov_, May 06 2015

%E a(10), a(20)-a(35) from _Chai Wah Wu_, Jan 21 2016