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

0,3

Comments

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

Links

Table of n, a(n) for n=0..33.

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

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)

Crossrefs

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

Sequence in context: A049958 A298403 A177487 * A076993 A076698 A323598

Adjacent sequences: A153007 A153008 A153009 * A153011 A153012 A153013

Keyword

nonn

Author

Omar E. Pol, Dec 21 2008

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

Status

approved