A094389 Last decimal digit of the odd Catalan number A038003(n).

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

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 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. - Franklin T. Adams-Watters, Feb 07 2006

Adams-Watters' surely-true 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: A200283 A355178 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