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

%I A336963 #10 Aug 11 2020 01:25:28
%S A336963 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,
%T A336963 20,19,24,23,16,31,62,61,58,57,54,53,50,49,46,45,42,41,38,37,34,33,60,
%U A336963 59,52,51,44,43,36,35,56,55,40,39,48,47,32,63,126,125,122
%N A336963 Left-rotate run-lengths of consecutive equal digits in binary representation of n.
%C A336963 This sequence is a permutation of the nonnegative integers, with inverse A336962.
%H A336963 Rémy Sigrist, <a href="/A336963/b336963.txt">Table of n, a(n) for n = 0..8191</a>
%H A336963 Rémy Sigrist, <a href="/A336963/a336963.png">Colored scatterplot of the first 2^16 terms</a> (where the color is function of A090996(n))
%H A336963 <a href="/index/Bi#binary">Index entries for sequences related to binary expansion of n</a>
%H A336963 <a href="/index/Per#IntegerPermutation">Index entries for sequences that are permutations of the natural numbers</a>
%F A336963 a(n) = n iff n = 0 or n belongs to A140690.
%e A336963 The first terms, in decimal and in binary, are:
%e A336963   n   a(n)  bin(n)  bin(a(n))
%e A336963   --  ----  ------  ---------
%e A336963    0     0       0          0
%e A336963    1     1       1          1
%e A336963    2     2      10         10
%e A336963    3     3      11         11
%e A336963    4     6     100        110
%e A336963    5     5     101        101
%e A336963    6     4     110        100
%e A336963    7     7     111        111
%e A336963    8    14    1000       1110
%e A336963    9    13    1001       1101
%e A336963   10    10    1010       1010
%e A336963   11     9    1011       1001
%e A336963   12    12    1100       1100
%e A336963   13    11    1101       1011
%e A336963   14     8    1110       1000
%e A336963   15    15    1111       1111
%o A336963 (PARI) toruns(n) = { my (r=[]); while (n, my (v=valuation(n+n%2,2)); n\=2^v; r=concat(v,r)); r }
%o A336963 fromruns(r) = { my (v=0); for (k=1, #r, v=(v+k%2)*2^r[k]-k%2); v }
%o A336963 a(n) = { my (r=toruns(n)); fromruns(vector(#r, k, r[1+k%#r])) }
%Y A336963 Cf. A006257, A090996, A101211, A140690, A336962.
%K A336963 nonn,base
%O A336963 0,3
%A A336963 _Rémy Sigrist_, Aug 09 2020