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

Author

Eric W. Weisstein, Apr 28 2004

Keywords

• nonn
• base

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

• Eric Weisstein's World of Mathematics, Catalan Number

Crossrefs

Cf. A000108, A038003.

Programs

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 *)

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