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a(n) is the smallest number which is the sum of two positive n-gonal numbers in more than one way.
2

%I #41 Oct 21 2023 01:48:45

%S 16,50,211,384,470,1053,1500,2242,3197,3277,5501,6780,8710,9896,10584,

%T 15198,15395,21237,23346,28696,33596,37725,40795,48474,55369,54146,

%U 69113,75732,84962,92541,95623,98672,123575,127317,146639,141066,154975,173416,201032

%N a(n) is the smallest number which is the sum of two positive n-gonal numbers in more than one way.

%C The sequence is not monotonically increasing as a(27) = 55369 > 54146 = a(28).

%H Chai Wah Wu, <a href="/A199809/b199809.txt">Table of n, a(n) for n = 3..2628</a>

%e a(3)=16 since 16=1+15=6+10, such that 1,15,6,10 are all triangular numbers (A000217) and there are no other positive numbers less than 16 with such a property.

%Y Cf. A000217.

%K nonn

%O 3,1

%A _Vladimir Shevelev_, Dec 16 2013

%E More terms from _Peter J. C. Moses_, Dec 16 2013