A260677 - OEIS

%I #25 Sep 08 2022 08:46:13

%S 1,1,1,3,7,17,35,74,150,304,612,1228,2460,4926,9857,19721,39449,78905,

%T 157818,315644,631296,1262601,2525212,5050435,10100879,20201769,

%U 40403550,80807112,161614235,323228483,646456979,1292913972,2585827958,5171655931,10343311876

%N a(n) = number of decimal digits in the n-th odd Catalan number A038003(n).

%H Jon E. Schoenfield, <a href="/A260677/b260677.txt">Table of n, a(n) for n = 0..1000</a>

%t Table[Floor[Log[CatalanNumber[2^n - 1]]/Log[10]] + 1, {n, 0, 27}]

%t f[n_] := Floor[(LogGamma[2^(n + 1) - 1] - 2*LogGamma[2^n] - n*Log[2])/Log[10]] + 1; Array[f, 34, 0] (* _Robert G. Wilson v_, Nov 21 2015 *)

%o (Magma) [Floor((LogGamma(2^(j+1)-1)-2*LogGamma(2^j)-Log(2^j))/Log(10))+1: j in [0..34]]; // _Jon E. Schoenfield_, Nov 21 2015

%o (Magma) [Floor(Log(Catalan(2^n-1))/Log(10)) + 1: n in [0..20]]; // _Vincenzo Librandi_, Nov 22 2015

%Y Cf. A000108, A038003.

%K nonn,base

%O 0,4

%A _L. Edson Jeffery_, Nov 15 2015

%E a(28)-a(34) from _Jon E. Schoenfield_, Nov 21 2015