A336963 Left-rotate run-lengths of consecutive equal digits in binary representation of n.

0, 1, 2, 3, 6, 5, 4, 7, 14, 13, 10, 9, 12, 11, 8, 15, 30, 29, 26, 25, 22, 21, 18, 17, 28, 27, 20, 19, 24, 23, 16, 31, 62, 61, 58, 57, 54, 53, 50, 49, 46, 45, 42, 41, 38, 37, 34, 33, 60, 59, 52, 51, 44, 43, 36, 35, 56, 55, 40, 39, 48, 47, 32, 63, 126, 125, 122

Offset

0,3

Comments

This sequence is a permutation of the nonnegative integers, with inverse A336962.

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 A090996(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    13    1001       1101
  10    10    1010       1010
  11     9    1011       1001
  12    12    1100       1100
  13    11    1101       1011
  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%#r])) }

Crossrefs

Cf. A006257, A090996, A101211, A140690, A336962.

Sequence in context: A336962 A342102 A284460 * A175949 A166404 A337242

Adjacent sequences: A336960 A336961 A336962 * A336964 A336965 A336966

Keyword

nonn,base

Author

Rémy Sigrist, Aug 09 2020

Status

approved