login
A336963
Left-rotate run-lengths of consecutive equal digits in binary representation of n.
2
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.
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
KEYWORD
nonn,base
AUTHOR
Rémy Sigrist, Aug 09 2020
STATUS
approved