

A094389


Last decimal digit of the odd Catalan number A038003(n).


4



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
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OFFSET

1,3


COMMENTS

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 nonfinal 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.  Franklin T. AdamsWatters, Feb 07 2006
AdamsWatters' surelytrue statement verified for n < 50000.  David J. Rusin, Apr 21 2009


LINKS

Table of n, a(n) for n=1..105.
Eric Weisstein's World of Mathematics, Catalan Number


MATHEMATICA

(* first do *) Needs["DiscreteMath`CombinatorialFunctions`"] (* then *) Table[ Mod[ CatalanNumber[2^n  1], 10], {n, 23}] (* 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}] (* Robert G. Wilson v, May 15 2004 *)


CROSSREFS

Cf. A000108, A038003.
Sequence in context: A117014 A200283 A010720 * A057821 A133742 A134879
Adjacent sequences: A094386 A094387 A094388 * A094390 A094391 A094392


KEYWORD

nonn,base


AUTHOR

Eric W. Weisstein, Apr 28 2004


EXTENSIONS

a(23) from Robert G. Wilson v, May 07 2004
a(24) & a(25) from Eric W. Weisstein, May 08 2004
a(26)a(30) from Robert G. Wilson v, May 15 2004
More terms from David Wasserman, May 07 2007


STATUS

approved



