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Search: id:A094389
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| 1, 1, 5, 9, 5, 9, 5, 9, 7, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5
(list; graph; listen)
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OFFSET
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1,3
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COMMENT
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Seems to be 5 for k >= 9.
C_n is divisible by 5 whenever the base 5 expansion of n+1 contains a 4 or a non-final 3. The assertion that this sequence is 5 for n>=9 is thus equivalent to asserting that 2^n contains such a base 5 digit for n>=9. This is almost certainly true. - Frank Adams-Watters (FrankTAW(AT)Netscape.net), Feb 07 2006
Adams-Watters' surely-true statement verified for n < 50000. [From Dave Rusin (rusin(AT)math.niu.edu), Apr 21 2009]
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LINKS
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Eric Weisstein's World of Mathematics, Catalan Number
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MATHEMATICA
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(* first do *) Needs["DiscreteMath`CombinatorialFunctions`"] (* then *) Table[ Mod[ CatalanNumber[2^n - 1], 10], {n, 23}] (from Robert G. Wilson v) (* or *)
exp[fact_, num_] := Block[{k = 1, t = 0}, While[s = Floor[fact/num^k]; s > 0, t = t + s; k++ ]; t]; f[n_] := Block[{k = 2, m = 1}, While[p = Prime[k]; p <= n, m = Mod[m*p^(exp[2n, p] - 2exp[n, p]), 10]; k++ ]; While[p = Prime[k]; p < 2n, m = Mod[m*p, 10]; k++ ]; m]; Table[ f[2^n - 1], {n, 26}] (from Robert G. Wilson v May 15 2004)
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CROSSREFS
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Cf. A000108, A038003.
Sequence in context: A108781 A117014 A010720 this_sequence A057821 A133742 A134879
Adjacent sequences: A094386 A094387 A094388 this_sequence A094390 A094391 A094392
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KEYWORD
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nonn,base
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AUTHOR
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Eric Weisstein (eric(AT)weisstein.com), Apr 28, 2004
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EXTENSIONS
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a(23) from Robert G. Wilson v (rgwv(AT)rgwv.com), May 07 2004
a(24) & a(25) from Eric Weisstein (eric(AT)weisstein.com), May 08 2004
a(26) through a(30) from Robert G. Wilson v (rgwv(AT)rgwv.com), May 15 2004
More terms from David Wasserman (dwasserm(AT)earthlink.net), May 07 2007
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