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A191765
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Integers that are a sum of two nonzero triangular numbers and also the sum of two nonzero square numbers.
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1
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2, 13, 18, 20, 25, 29, 34, 37, 58, 61, 65, 72, 73, 90, 97, 100, 101, 106, 130, 136, 137, 146, 148, 157, 160, 164, 169, 181, 193, 200, 202, 205, 208, 218, 225, 226, 232, 234, 241, 244, 245, 265, 272, 274, 277, 281, 288, 289, 298, 306, 328, 340, 346, 353, 370, 373, 388, 389, 400
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OFFSET
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1,1
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COMMENTS
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LINKS
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P. A. Piza, G. W. Walker and C. M. Sandwick, Sr, Problem 4425, The American Mathematical Monthly, Vol. 59, No. 6, (June - July 1952), pp. 417-419.
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EXAMPLE
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25 is the sum of two nonzero triangular numbers: 10 + 15, and of two nonzero squares: 9 + 16; so 25 is in the sequence.
9 is the sum of two nonzero triangular numbers: 3 + 6, but can be represented as the sum of two squares only using zero: 0 + 9; so 9 is not in the sequence.
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MATHEMATICA
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data=Length[Reduce[a^2+b^2==1/2 c (c+1)+1/2 d(d+1)== # && a>0 && b>0 && c>0 && d>0, {a, b, c, d}, Integers]] &/@Range[400]; DeleteCases[Table[If[data[[k]]>0, k, 0], {k, 1, Length[data]}], 0]
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CROSSREFS
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KEYWORD
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nonn,easy
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AUTHOR
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STATUS
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approved
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