%I #27 Feb 18 2024 01:34:15
%S 0,1,2,2,3,3,3,3,3,4,4,4,4,4,4,4,4,4,4,4,4,4,4,5,5,5,5,5,5,5,5,5,5,5,
%T 5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,6,6,6,
%U 6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6
%N Half of the binary width of the terms of A014486, the number of digits in A063171(n)/2.
%H Paolo Xausa, <a href="/A072643/b072643.txt">Table of n, a(n) for n = 0..10000</a>
%F Sum_{n>=1} (-1)^(n+1)/a(n) = Sum_{n>=1} (-1)^(n+1)/(2^n-1) = 0.76449978034844420919... . - _Amiram Eldar_, Feb 18 2024
%t a[n_] := Module[{i, c, a}, i = c = 0; a = 1; While[n>c, a *= (4*i+2)/(i+2); i++; c += a]; i];
%t Table[a[n], {n, 0, 104}] (* _Jean-François Alcover_, Dec 26 2017, from Sage code *)
%t Flatten[Array[Table[#, CatalanNumber[#]]&, 7, 0]] (* _Paolo Xausa_, Feb 13 2024 *)
%o (Sage)
%o def A072643(n) :
%o i = c = 0; a = 1
%o while n > c :
%o a *= (4*i+2)/(2+i)
%o i += 1; c += a
%o return i
%o [A072643(n) for n in (0..100)] # _Peter Luschny_, Sep 07 2012
%Y Each value v occurs A000108(v) times. The maximum position for value v to occur is A014138(v). Permutations: A071673, A072644, A072645, A072660. Cf. also A002024, A072649.
%K nonn,base
%O 0,3
%A _Antti Karttunen_, Jun 02 2002