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 A191765 Integers that are a sum of two nonzero triangular numbers and also the sum of two nonzero square numbers. 1
 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 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,1 COMMENTS A134422 is a subsequence. - Franklin T. Adams-Watters, Jun 25 2011 LINKS P. A. Piza, Problems for Solution: 4425, The American Mathematical Monthly, Vol. 58, No. 2, (February 1951), p. 113. 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. EXAMPLE 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. MATHEMATICA 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] CROSSREFS Cf. A000217, A000290, A191766, intersection of A000404 and A051533, A134422. Sequence in context: A175448 A067522 A128852 * A063615 A297837 A246358 Adjacent sequences:  A191762 A191763 A191764 * A191766 A191767 A191768 KEYWORD nonn,easy AUTHOR Ant King, Jun 22 2011 STATUS approved

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Last modified August 11 06:25 EDT 2020. Contains 336422 sequences. (Running on oeis4.)