A191765 Integers that are a sum of two nonzero triangular numbers and also the sum of two nonzero square numbers.

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

Offset

1,1

Comments

A134422 is a subsequence. - Franklin T. Adams-Watters, Jun 25 2011

Links

Table of n, a(n) for n=1..59.

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