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Search: id:A084702
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| A084702 |
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a(n) = smallest k such that k+1 and nk+1 both are perfect squares, or 0 if no such number exists. |
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+0
9
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| 3, 24, 8, 0, 3, 8, 24, 3, 0, 8, 48, 24, 15, 120, 8, 3, 15, 168, 80, 48, 3, 24, 360, 15, 0, 24, 440, 8, 120, 80, 120, 195, 3, 840, 24, 8, 35, 960, 440, 3, 168, 120, 168, 28560, 8, 48, 1680, 35, 0, 48, 24, 120, 483, 175560, 8, 3, 24, 528, 212520, 728, 63, 3024
(list; graph; listen)
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OFFSET
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1,1
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COMMENT
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a(4) = a(9) = 0 as when k=1 is a square 4k +4 is also a square hence 4k+1 can not be a square for k > 0.
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LINKS
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David Wasserman (dwasserm(AT)earthlink.net), May 03 2007, Table of n, a(n) for n = 1..100
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FORMULA
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a(i^2-1) is usually (i-1)^2-1. For 2 < i < 1000 there are 34 exceptions. The first four of these are a(11^2-1) = 3, a(23^2-1) = 8, a(39^2-1) = 15, and a(41^2-1) = 3. - David Wasserman (dwasserm(AT)earthlink.net), May 03 2007
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EXAMPLE
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a(5) = 3 as 3 + 1 = 4 and 3*5 + 1 = 16 both are squares.
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CROSSREFS
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Cf. A084703.
Adjacent sequences: A084699 A084700 A084701 this_sequence A084703 A084704 A084705
Sequence in context: A062834 A002980 A047980 this_sequence A065430 A035409 A081312
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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 08 2003
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EXTENSIONS
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More terms from Donald Sampson (marsquo(AT)hotmail.com), Dec 04 2003
Corrected by David Wasserman, May 03 2007
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