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A178746 Binary counter with intermittent bits. Starting at zero the counter attempts to increment by 1 at each step but each bit in the counter alternately accepts and rejects requests to toggle. 3
0, 1, 3, 6, 6, 7, 13, 12, 12, 13, 15, 26, 26, 27, 25, 24, 24, 25, 27, 30, 30, 31, 53, 52, 52, 53, 55, 50, 50, 51, 49, 48, 48, 49, 51, 54, 54, 55, 61, 60, 60, 61, 63, 106, 106, 107, 105, 104 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,3

COMMENTS

A simple scatter plot reveals a self-similar structure that resembles flying geese.

Ignoring the initial zero term, split the sequence into rows of increasing binary magnitude such that the terms in row m satisfy 2^m <= a(n) < 2^(m+1).

0: 1,

1: 3,

2: 6,6,7,

3: 13,12,12,13,15,

4: 26,26,27,25,24,24,25,27,30,30,31,

5: 53,52,52,53,55,50,50,51,49,48,48,49,51,54,54,55,61,60,60,61,63,

Then,

Row m starts at n = A005578(m+1) in the original sequence

The first term in row m is A081254(m)

The last term in row m is 2^(m+1)-1

The number of terms in row m is A001045(m+1)

The number of distinct terms in row m is A005578(m)

The number of ascending runs in row m is A005578(m)

The number of non-ascending runs in row m is A005578(m)

The number of descending runs in row m is A052950(m)

The number of non-descending runs in row m is A005578(m-1)

The sum of terms in row m is A178747(m)

The total number of '1' bits in the terms of row n is A178748(m)

LINKS

D. Scambler, Table of n, a(n) for n = 0..1024

FORMULA

If n is a power of 2, a(n) = n*3/2. Lim(a(n)/n) = 3/2.

EXAMPLE

0 -> low bit toggles -> 1 -> should be 2 but low bit does not toggle -> 3 -> should be 4 but 2nd-lowest bit does not toggle -> 6 -> should be 7 but low bit does not toggle -> 6 -> low bit toggles -> 7

PROG

(PARI) seq(n)={my(a=vector(n+1), f=0, p=0); for(i=2, #a, my(b=bitxor(p+1, p)); f=bitxor(f, b); p=bitxor(p, bitand(b, f)); a[i]=p); a} \\ Andrew Howroyd, Mar 03 2020

CROSSREFS

Cf. A178747 sum of terms in rows of a(n), A178748 total number of '1' bits in the terms of rows of a(n).

Sequence in context: A239318 A177783 A228945 * A229986 A025500 A141218

Adjacent sequences:  A178743 A178744 A178745 * A178747 A178748 A178749

KEYWORD

nonn,look

AUTHOR

David Scambler, Jun 08 2010

STATUS

approved

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Last modified May 30 18:38 EDT 2020. Contains 334728 sequences. (Running on oeis4.)