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Search: id:A094353
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| A094353 |
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Smallest integer not yet used such that 1 + Product_{k=1}^n a(k) is a square. |
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+0
2
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OFFSET
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1,1
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COMMENT
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a(11), if it exists, is > 10000. This sequence does not include every natural number. Suppose it contains b^2. Then letting A be the product up to b^2, we have A + 1 = i^2, and b^2 A + 1 = j^2. Multiplying the first equation by b^2 and subtracting, we get (bi)^ = j^2 + b^2 - 1, which puts an upper bound on i and j (and hence on A). Probably the sequence contains no squares other than 1. Question: is this sequence infinite? - Frank Adams-Watters (FrankTAW(AT)Netscape.net), Aug 29 2006
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EXAMPLE
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3+1= 4, 3*1*5 +1 = 16, 3*1*5*8 +1 = 121 etc. are squares.
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CROSSREFS
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Cf. A094354.
Sequence in context: A116647 A063858 A124420 this_sequence A129801 A128821 A029723
Adjacent sequences: A094350 A094351 A094352 this_sequence A094354 A094355 A094356
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KEYWORD
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more,nonn
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AUTHOR
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Amarnath Murthy (amarnath_murthy(AT)yahoo.com), May 22 2004
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EXTENSIONS
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More terms from Frank Adams-Watters (FrankTAW(AT)Netscape.net), Aug 29 2006
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