A151568 a(0)=1, a(1)=1; a(2^i+j)=2*a(j)+a(j+1) for 0 <= j < 2^i.

1, 1, 3, 5, 3, 5, 11, 13, 3, 5, 11, 13, 11, 21, 35, 29, 3, 5, 11, 13, 11, 21, 35, 29, 11, 21, 35, 37, 43, 77, 99, 61, 3, 5, 11, 13, 11, 21, 35, 29, 11, 21, 35, 37, 43, 77, 99, 61, 11, 21, 35, 37, 43, 77, 99, 69, 43, 77, 107, 117, 163, 253, 259, 125, 3, 5, 11, 13, 11, 21, 35, 29, 11

Offset: 0

Author

N. J. A. Sloane, May 25 2009

Keywords

• nonn

Comments

Equals A160552+A151704.

Links

• Ivan Neretin, Table of n, a(n) for n = 0..8191
• David Applegate, Omar E. Pol and N. J. A. Sloane, The Toothpick Sequence and Other Sequences from Cellular Automata, Congressus Numerantium, Vol. 206 (2010), 157-191. [There is a typo in Theorem 6: (13) should read u(n) = 4.3^(wt(n-1)-1) for n >= 2.]
• N. J. A. Sloane, Catalog of Toothpick and Cellular Automata Sequences in the OEIS

Crossrefs

For the recurrence a(2^i+j) = C*a(j) + D*a(j+1), a(0) = A, a(1) = B for following values of (A B C D) see: (0 1 1 1) A118977, (1 0 1 1) A151702, (1 1 1 1) A151570, (1 2 1 1) A151571, (0 1 1 2) A151572, (1 0 1 2) A151703, (1 1 1 2) A151573, (1 2 1 2) A151574, (0 1 2 1) A160552, (1 0 2 1) A151704, (1 1 2 1) A151568, (1 2 2 1) A151569, (0 1 2 2) A151705, (1 0 2 2) A151706, (1 1 2 2) A151707, (1 2 2 2) A151708.

Cf. A139250, A160552, A151569.

Programs

Mathematica

a = {1, 1}; Do[AppendTo[a, 2 a[[j]] + a[[j + 1]]], {i, 6}, {j, 2^i}]; a (* Ivan Neretin, Jul 04 2017 *)