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

Offset: 1

Author

Leroy Quet, Jul 29 2009

Keywords

• base
• nonn
• tabf

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.

Examples

			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;
		

Links

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

Crossrefs

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

Equals A228351-1, termwise.

Programs

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 *)

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

Scheme

(define (A163510 n) (- (A227186bi (A006068 (A100922 (- n 1))) (A243067 n)) 1))
;; See A227186 for A227186bi. - Antti Karttunen, Jun 19 2014

Formula

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

Extensions

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