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A194688 First differences of A036554 (numbers whose binary representation ends in an odd number of zeros). 0
4, 2, 2, 4, 4, 4, 2, 2, 4, 2, 2, 4, 2, 2, 4, 4, 4, 2, 2, 4, 4, 4, 2, 2, 4, 4, 4, 2, 2, 4, 2, 2, 4, 2, 2, 4, 4, 4, 2, 2, 4, 2, 2, 4, 2, 2, 4, 4, 4, 2, 2, 4, 2, 2, 4, 2, 2, 4, 4, 4, 2, 2, 4, 4, 4, 2, 2, 4, 4, 4, 2, 2, 4, 2, 2, 4, 2, 2, 4, 4, 4, 2, 2, 4, 4, 4, 2, 2, 4, 4, 4, 2, 2, 4, 2, 2, 4, 2, 2, 4, 4, 4, 2, 2, 4, 4, 4, 2, 2, 4, 4, 4, 2, 2, 4, 2, 2, 4, 2, 2, 4, 4, 4, 2, 2, 4, 2, 2, 4, 2, 2, 4, 4, 4, 2, 2, 4, 2 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

COMMENTS

Conjecture. This sequence is self-generated according to the following rule: start with {4} at step 0, then extend by steps, appending {2,2,4} at step n if a(n)=4 or appending {4} if a(n)=2. (This has been verified for several thousand terms.) To illustrate, the first few steps of this process give {4}->{4,2,2,4}, since a(1)=4, ->{4,2,2,4,4}, since a(2)=2, ->{4,2,2,4,4,4}, since a(3)=2,->{{4,2,2,4,4,4,2,2,4}, since a(4)=4, etc. Equivalently, it appears that {a(n)} is the fixed-point of the morphism 2->4, 4->422, starting with 4.

Since A036554 = 2*A003159, this conjecture follows from the paper by Allouche, Shallit and Skordev in 2005, see page 13. - Michel Dekking, Jan 06 2019

It appears that arbitrarily long runs of terms of this sequence occur in A023630 and A023632.

LINKS

Table of n, a(n) for n=1..138.

J.-P. Allouche, J. Shallit and G. Skordev, Self-generating sets, integers with missing blocks and substitutions, Discrete Math. 292 (2005) 1-15.

MATHEMATICA

Differences[Select[Range[500], OddQ[IntegerExponent[#, 2]]&]] (* Harvey P. Dale, Jun 29 2021 *)

CROSSREFS

Cf. A003159, A036554.

Cf. A023630, A023632.

Sequence in context: A170988 A141035 A100854 * A317389 A322510 A021707

Adjacent sequences: A194685 A194686 A194687 * A194689 A194690 A194691

KEYWORD

nonn

AUTHOR

John W. Layman, Sep 03 2011

STATUS

approved

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Last modified January 29 13:51 EST 2023. Contains 359923 sequences. (Running on oeis4.)