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Search: id:A080663
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| A080663 |
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Numbers of the form 3n^2 - 1. |
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+0
4
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| 2, 11, 26, 47, 74, 107, 146, 191, 242, 299, 362, 431, 506, 587, 674, 767, 866, 971, 1082, 1199, 1322, 1451, 1586, 1727, 1874, 2027, 2186, 2351, 2522, 2699, 2882, 3071, 3266, 3467, 3674, 3887, 4106, 4331, 4562, 4799, 5042, 5291, 5546, 5807, 6074, 6347, 6626
(list; graph; listen)
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OFFSET
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1,1
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COMMENT
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These numbers cannot be perfect squares. See the link for a proof.
2nd elementary symmetric polynomial of n,n+1,and n+2: n(n+1)+n(n+2)+(n+1)(n+2). - Zak Seidov (zakseidov(AT)yahoo.com), Mar 23 2005
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REFERENCES
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E. Grosswald, Topics from the Theory of Numbers, 1966 p 64 problem 11
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LINKS
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Cino Hilliard, 3n^2-1 not square .
Eric Weisstein's World of Mathematics, Symmetric Polynomial
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FORMULA
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a(n) = unsigned real term in (1 + ni)^3. E.g. (1 + 4i)^3 = (-47 - 52i); where 52 = A121670(4). Note that (4 + i)^3 = (52 + 47i) = (A121670(4) + A080663(4)i). - Gary W. Adamson (qntmpkt(AT)yahoo.com), Aug 14 2006
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PROGRAM
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(PARI) nosquare(n) = { for(x=1, n, y = 3*x*x-1; print1(y" ") ) } checkit(n) = { for(x=1, n, y = 3*x*x-1; if(!issquare(y), print1(y" ")) ) }
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CROSSREFS
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Cf. A121670.
Sequence in context: A012251 A077482 A104085 this_sequence A139211 A054552 A034534
Adjacent sequences: A080660 A080661 A080662 this_sequence A080664 A080665 A080666
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KEYWORD
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easy,nonn
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AUTHOR
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Cino Hilliard (hillcino368(AT)gmail.com), Mar 01 2003
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