cp's OEIS Frontend

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

%I A094389 #16 Feb 16 2025 08:32:53
%S A094389 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,
%T A094389 5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,
%U A094389 5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5
%N A094389 Last decimal digit of the odd Catalan number A038003(n).
%C A094389 Seems to be 5 for k >= 9.
%C A094389 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
%C A094389 Adams-Watters' surely-true statement verified for n < 50000. - _David J. Rusin_, Apr 21 2009
%H A094389 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/CatalanNumber.html">Catalan Number</a>
%t A094389 (* first do *) Needs["DiscreteMath`CombinatorialFunctions`"] (* then *) Table[ Mod[ CatalanNumber[2^n - 1], 10], {n, 23}] (* _Robert G. Wilson v_ *) (* or *)
%t A094389 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 *)
%Y A094389 Cf. A000108, A038003.
%K A094389 nonn,base
%O A094389 1,3
%A A094389 _Eric W. Weisstein_, Apr 28 2004
%E A094389 a(23) from _Robert G. Wilson v_, May 07 2004
%E A094389 a(24) & a(25) from _Eric W. Weisstein_, May 08 2004
%E A094389 a(26)-a(30) from _Robert G. Wilson v_, May 15 2004
%E A094389 More terms from _David Wasserman_, May 07 2007