A139477 Number of binary digits in A001109(n).

1, 1, 3, 6, 8, 11, 13, 16, 18, 21, 23, 26, 29, 31, 34, 36, 39, 41, 44, 46, 49, 51, 54, 56, 59, 62, 64, 67, 69, 72, 74, 77, 79, 82, 84, 87, 90, 92, 95, 97, 100, 102, 105, 107, 110, 112, 115, 118, 120, 123, 125, 128, 130, 133, 135, 138, 140, 143, 146, 148, 151, 153, 156, 158, 161, 163, 166, 168

Offset: 0

Author

Artur Jasinski, Apr 22 2008

Keywords

• base
• nonn

Links

• Robert Israel, Table of n, a(n) for n = 0..10000

Crossrefs

Cf. A001109, A139473, A139474, A139475, A139476, A139478.

Programs

Maple

a[0]:= 0: a[1]:= 1: R[0]:= 1: R[1]:= 1:
for n from 2 to 100 do
   a[n]:=  6*a[n-1] - a[n-2];
   R[n]:= ilog2(a[n])+1;
od:
seq(R[i],i=0..100); # Robert Israel, Nov 23 2024

Mathematica

a = {}; Do[k = Length[IntegerDigits[Expand[((2*Sqrt[2] + 3)^(n) - (3 - 2*Sqrt[2])^(n))/(4*Sqrt[2])], 2]]; Print[k]; AppendTo[a, k], {n, 1, 50}]; a
Rest[IntegerLength[#,2]&/@LinearRecurrence[{6,-1},{0,1},60]] (* Harvey P. Dale, Feb 11 2015 *)

Formula

a(n) = A070939(A001109(n)). - Michel Marcus, Nov 02 2013

Extensions

Incorrect link to index entries for linear recurrences with constant coefficients removed by Colin Barker, Oct 13 2015

a(0) = 1 prepended and more terms by Robert Israel, Nov 23 2024