A153010 Indices of A153007 where the entry equals zero.

0, 1, 2, 3, 7, 15, 31, 63, 127, 255, 511, 1023, 2047, 4095, 8191, 16383, 32767, 65535, 131071, 262143, 524287, 1048575, 2097151, 4194303, 8388607, 16777215, 33554431, 67108863, 134217727, 268435455, 536870911, 1073741823, 2147483647, 4294967295

Offset: 0

Author

Omar E. Pol, Dec 21 2008

Keywords

• nonn

Comments

It appears that this sequence is also the union of 2 and A000225. - Omar E. Pol, Mar 03 2011

Links

• 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

Cf. A000217, A000225, A139250, A153006, A153007.

Formula

Conjectures from Colin Barker, Nov 24 2019: (Start)

G.f.: x*(1 - x - x^2 + 2*x^3) / ((1 - x)*(1 - 2*x)).

a(n) = 3*a(n-1) - 2*a(n-2) for n>4.

a(n) = 2^(n-1) - 1 for n>2.

(End)

Extensions

More terms a(7)-a(18) from Sean A. Irvine, Feb 22 2011

More terms a(19)-a(33) from Omar E. Pol, Mar 03 2011