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
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
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.
Comments