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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
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.
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
Sequence in context: A362399 A080823 A117925 * A138394 A140752 A246780
KEYWORD
nonn
AUTHOR
John W. Layman, Feb 23 2008
STATUS
approved