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A128549
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Difference between triangular number and next perfect square.
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0
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3, 1, 3, 6, 1, 4, 8, 13, 4, 9, 15, 3, 9, 16, 1, 8, 16, 25, 6, 15, 25, 3, 13, 24, 36, 10, 22, 35, 6, 19, 33, 1, 15, 30, 46, 10, 26, 43, 4, 21, 39, 58, 15, 34, 54, 8, 28, 49, 71, 21, 43, 66, 13, 36, 60, 4, 28, 53, 79, 19, 45, 72, 9, 36, 64, 93, 26, 55, 85, 15, 45, 76, 3, 34, 66, 99, 22
(list; graph; refs; listen; history; internal format)
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OFFSET
| 1,1
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COMMENTS
| If a(n)=1 then such n gives the sequence A006451 (triangular numbers whose distance to the nearest bigger perfect square is 1). [From Ctibor O. ZIZKA (c.zizka(AT)email.cz), Oct 07 2009]
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FORMULA
| a(n)=(floor(sqrt(n(n+1)/2))+1)^2-n(n+1)/2
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EXAMPLE
| a(1)=2^2-1(1+1)/2=3, a(2)=2^2-2(2+1)/2=1, a(3)=3^2-3(3+1)/2=3, a(3)=4^2-4(4+1)/2=6.
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MATHEMATICA
| Table[(Floor[Sqrt[n(n+1)/2]]+1)^2-n(n+1)/2, {n, 100}]
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CROSSREFS
| Cf. A000217.
Sequence in context: A049324 A181843 A131111 * A055885 A181425 A174505
Adjacent sequences: A128546 A128547 A128548 * A128550 A128551 A128552
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KEYWORD
| nonn
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AUTHOR
| Zak Seidov (zakseidov(AT)yahoo.com), May 08 2007
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