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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
KEYWORD
nonn,easy
AUTHOR
Ant King, Jun 22 2011
STATUS
approved

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Last modified July 14 22:52 EDT 2024. Contains 374323 sequences. (Running on oeis4.)