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Search: id:A072470
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| A072470 |
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a(0) = 0, a(1) = 9; for n > 1 a(n) = smallest positive square (possibly required to be greater than a(n-1)?) such that a(0) + a(1) + ... + a(n) is a square. |
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+0
3
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| 0, 9, 16, 144, 7056, 17424, 151880976, 3370896, 11141224704, 65067847056, 39037856400, 107295207555600, 189756686048400, 3749779657193648400, 2631616745340978864144, 15179712895673097530256
(list; graph; listen)
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OFFSET
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0,2
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COMMENT
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Sequence is infinite as every partial sum (n>0) is odd, say 2k + 1 and then k^2 is a candidate for the next term.
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FORMULA
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a(n) = A018930(n)^2. - Benoit Cloitre, Jun 21 2002
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EXAMPLE
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a(3) = 16 as a(1) + a(2) + a(3) = 25 is also a square. a(4) = 144 as 0 + 9 + 16 + 144 = 169 is also a square.
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MATHEMATICA
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a[0] = 0; a[1] = 9; a[n_] := a[n] = (k = Sqrt[a[n - 1]] + 1; s = Sum[a[i], {i, 0, n - 1}]; While[ !IntegerQ[ Sqrt[s + k^2]], k++ ]; k^2);
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CROSSREFS
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Sequence in context: A014720 A138238 A075373 this_sequence A053911 A050802 A136313
Adjacent sequences: A072467 A072468 A072469 this_sequence A072471 A072472 A072473
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KEYWORD
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nonn
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AUTHOR
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Amarnath Murthy (amarnath_murthy(AT)yahoo.com), Jun 19 2002
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EXTENSIONS
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Edited by N. J. A. Sloane (njas(AT)research.att.com) and Robert G. Wilson v (rgwv(AT)rgwv.com), Jun 21 2002
More terms from Benoit Cloitre (benoit7848c(AT)orange.fr), Jun 21 2002
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