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Search: id:A111002
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| A111002 |
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a(n) = gcd( f(n), f(n+1)) where f(n) = n^4+n^2+1. |
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1
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| 1, 3, 7, 91, 21, 31, 43, 57, 73, 91, 777, 133, 157, 183, 211, 241, 273, 2149, 343, 381, 421, 463, 507, 553, 4207, 651, 703, 757, 813, 871, 931, 6951, 1057, 1123, 1191, 1261, 1333, 1407, 10381, 1561, 1641, 1723, 1807, 1893, 1981, 14497, 2163, 2257, 2353
(list; graph; listen)
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OFFSET
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0,2
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LINKS
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Author?, More information
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FORMULA
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a(n) = gcd(f(n), f(n+1)) for all n. a(n) = n^2+n+1, except when n congruent to 3 modulo 7 when a(n) = 7(n^2+n+1).
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EXAMPLE
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a(10) = 7(10^2+10+1) = 777 because 10 is congruent to 3 modulo 7.
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MATHEMATICA
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f[n_] := n^4 + n^2 + 1; Table[ GCD[f[n], f[n + 1]], {n, 0, 49}] (* Robert G. Wilson v *)
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PROGRAM
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(PARI) m=50; a=3; for(k=2, m, b=k^4+k^2+1; print1(gcd(a, b), ", "); a=b) (Brockhaus)
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CROSSREFS
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Sequence in context: A041705 A137130 A058379 this_sequence A042481 A088419 A062592
Adjacent sequences: A110999 A111000 A111001 this_sequence A111003 A111004 A111005
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KEYWORD
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easy,nonn
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AUTHOR
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Pahikkala Jussi (pahio(AT)wakkanet.fi), Sep 30 2005
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EXTENSIONS
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More terms from Robert G. Wilson v (rgwv(at)rgwv.com) and Klaus Brockhaus (klaus-brockhaus(AT)t-online.de), Oct 02 2005
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