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

Author

Rémy Sigrist, Aug 09 2020

Keywords

• nonn
• base

Comments

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

Examples

			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
		

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

Crossrefs

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

Programs

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])) }

Formula

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