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 A135571 Positive integers that are the difference of two positive triangular numbers in an odd number of ways. 1
 2, 3, 4, 6, 8, 9, 10, 15, 16, 18, 21, 25, 28, 32, 45, 49, 50, 55, 64, 66, 72, 78, 81, 91, 98, 100, 105, 120, 121, 128, 136, 144, 153, 162, 169, 171, 190, 196, 200, 210, 225, 231, 242, 253, 256, 276, 288, 289, 300, 324, 325, 338, 351, 361, 378, 392, 400, 406, 435 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,1 COMMENTS Conjecture. This sequence is just the sequence of positive integers that are either square, twice a square, or triangular, but not both square and triangular (A001110). (This has been verified for n up to 100000.) If the triangular number 0 is allowed, then Verhoeff has shown (see the reference) that the numbers that are the difference of two triangular numbers in exactly one way are just the powers of 2. LINKS EXAMPLE As differences of two positive triangular numbers, 6 =21-15 (1 way), 9 =10-1 =15-6 =45-36 (3 ways), so 6 and 9 are terms of the sequence; 5 =6-1 = 15-10 (2 ways), so 5 is not a term of the sequence. CROSSREFS Cf. A000217, A001110. Sequence in context: A303434 A080823 A117925 * A138394 A140752 A246780 Adjacent sequences: A135568 A135569 A135570 * A135572 A135573 A135574 KEYWORD nonn AUTHOR John W. Layman, Feb 23 2008 STATUS approved

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Last modified January 30 03:32 EST 2023. Contains 359939 sequences. (Running on oeis4.)