A163510 - OEIS

A163510

Irregular table read by rows: Write n in binary. For each 1, the m-th term of row n is the number of 0's between the m-th 1, reading right to left, and the (m-1)th 1 (or the right side of the number if m-1 = 0).

0, 1, 0, 0, 2, 0, 1, 1, 0, 0, 0, 0, 3, 0, 2, 1, 1, 0, 0, 1, 2, 0, 0, 1, 0, 1, 0, 0, 0, 0, 0, 0, 4, 0, 3, 1, 2, 0, 0, 2, 2, 1, 0, 1, 1, 1, 0, 1, 0, 0, 0, 1, 3, 0, 0, 2, 0, 1, 1, 0, 0, 0, 1, 0, 2, 0, 0, 0, 1, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 5, 0, 4, 1, 3, 0, 0, 3, 2, 2, 0, 1, 2, 1, 0, 2, 0, 0, 0, 2, 3, 1, 0, 2, 1, 1, 1, 1, 0, 0, 1, 1, 2, 0, 1, 0, 1, 0, 1, 1, 0, 0, 1

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OFFSET

1,5

COMMENTS

Row n contains exactly A000120(n) terms, for each n.

All odd-numbered rows begin with 0. All even-numbered rows begin with a positive integer.

Can be used to compute the permutation A163511.

LINKS

Antti Karttunen, Table of n, a(n) for n = 1..11265

FORMULA

a(n) = A227186(A006068(A100922(n-1)), A243067(n)) - 1. - Antti Karttunen, Jun 19 2014

EXAMPLE

Table begins as:

Row n in Terms on

n binary that row

1 1 0; (the distance of 1-bit from the right edge is zero)

2 10 1; (the distance of 1-bit from the right edge is one)

3 11 0,0;

4 100 2;

5 101 0,1; (the least significant 1-bit is zero steps away from the right edge, and there is one zero between those two 1-bits)

6 110 1,0;

7 111 0,0,0;

8 1000 3;

9 1001 0,2;

10 1010 1,1;

11 1011 0,0,1;

12 1100 2,0;

13 1101 0,1,0;

14 1110 1,0,0;

15 1111 0,0,0,0;

16 10000 4;

MATHEMATICA

Table[Reverse@ Map[Ceiling[(Length@ # - 1)/2] &, DeleteCases[Split@ Join[Riffle[IntegerDigits[n, 2], 0], {0}], {k__} /; k == 1]], {n, 46}] // Flatten (* Michael De Vlieger, Jul 25 2016 *)

PROG

(Scheme) (define (A163510 n) (- (A227186bi (A006068 (A100922 (- n 1))) (A243067 n)) 1))

;; See A227186 for A227186bi. - Antti Karttunen, Jun 19 2014

(Python)

from itertools import count, islice

def A163510_gen(): # generator of terms

for n in count(1):

k = n

while k:

yield (s:=(~k&k-1).bit_length())

k >>= s+1

A163510_list = list(islice(A163510_gen(), 30)) # Chai Wah Wu, Jul 17 2023

CROSSREFS

Cf. A000120, A006068, A100922, A227186, A243067, A163511, A227736.

Equals A228351-1, termwise.

Sequence in context: A103306 A269249 A182423 * A124735 A375202 A064874

Adjacent sequences: A163507 A163508 A163509 * A163511 A163512 A163513

KEYWORD

base,nonn,tabf

AUTHOR

Leroy Quet, Jul 29 2009

EXTENSIONS

Additional terms computed and Example section added by Antti Karttunen, Jun 19 2014

STATUS

approved