A072643 Half of the binary width of the terms of A014486, the number of digits in A063171(n)/2.

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, 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, 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

Offset: 0

Author

Antti Karttunen, Jun 02 2002

Keywords

• nonn
• base

Links

• Paolo Xausa, Table of n, a(n) for n = 0..10000

Crossrefs

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.

Programs

Mathematica

a[n_] := Module[{i, c, a}, i = c = 0; a = 1; While[n>c, a *= (4*i+2)/(i+2); i++; c += a]; i];
Table[a[n], {n, 0, 104}] (* Jean-François Alcover, Dec 26 2017, from Sage code *)
Flatten[Array[Table[#, CatalanNumber[#]]&, 7, 0]] (* Paolo Xausa, Feb 13 2024 *)

Sage

def A072643(n) :
    i = c = 0; a = 1
    while n > c :
        a *= (4*i+2)/(2+i)
        i += 1; c += a
    return i
[A072643(n) for n in (0..100)] # Peter Luschny, Sep 07 2012

Formula

Sum_{n>=1} (-1)^(n+1)/a(n) = Sum_{n>=1} (-1)^(n+1)/(2^n-1) = 0.76449978034844420919... . - Amiram Eldar, Feb 18 2024