A336962 Right-rotate run-lengths of consecutive equal digits in binary representation of n.

0, 1, 2, 3, 6, 5, 4, 7, 14, 11, 10, 13, 12, 9, 8, 15, 30, 23, 22, 27, 26, 21, 20, 29, 28, 19, 18, 25, 24, 17, 16, 31, 62, 47, 46, 55, 54, 45, 44, 59, 58, 43, 42, 53, 52, 41, 40, 61, 60, 39, 38, 51, 50, 37, 36, 57, 56, 35, 34, 49, 48, 33, 32, 63, 126, 95, 94

Offset

0,3

Comments

This sequence is a permutation of the nonnegative integers, with inverse A336963.

Links

Rémy Sigrist, Table of n, a(n) for n = 0..8191

Rémy Sigrist, Colored scatterplot of the first 2^16 terms (where the color is function of A136480(n))

Index entries for sequences related to binary expansion of n

Index entries for sequences that are permutations of the natural numbers

Formula

a(n) = n iff n = 0 or n belongs to A140690.

Example

The first terms, in decimal and in binary, are:
  n   a(n)  bin(n)  bin(a(n))
  --  ----  ------  ---------
   0     0       0          0
   1     1       1          1
   2     2      10         10
   3     3      11         11
   4     6     100        110
   5     5     101        101
   6     4     110        100
   7     7     111        111
   8    14    1000       1110
   9    11    1001       1011
  10    10    1010       1010
  11    13    1011       1101
  12    12    1100       1100
  13     9    1101       1001
  14     8    1110       1000
  15    15    1111       1111

Prog

(PARI) toruns(n) = { my (r=[]); while (n, my (v=valuation(n+n%2, 2)); n\=2^v; r=concat(v, r)); r }
fromruns(r) = { my (v=0); for (k=1, #r, v=(v+k%2)*2^r[k]-k%2); v }
a(n) = { my (r=toruns(n)); fromruns(vector(#r, k, r[1+(k-2)%#r])) }

Crossrefs

Cf. A038572, A101211, A136480, A140690, A336963 (inverse).

Sequence in context: A357523 A056539 A105726 * A342102 A284460 A336963

Adjacent sequences: A336959 A336960 A336961 * A336963 A336964 A336965

Keyword

nonn,base

Author

Rémy Sigrist, Aug 09 2020

Status

approved