cp's OEIS Frontend

A336962 Right-rotate run-lengths of consecutive equal digits in binary representation of n.

%I A336962 #11 Aug 11 2020 01:25:31
%S A336962 0,1,2,3,6,5,4,7,14,11,10,13,12,9,8,15,30,23,22,27,26,21,20,29,28,19,
%T A336962 18,25,24,17,16,31,62,47,46,55,54,45,44,59,58,43,42,53,52,41,40,61,60,
%U A336962 39,38,51,50,37,36,57,56,35,34,49,48,33,32,63,126,95,94
%N A336962 Right-rotate run-lengths of consecutive equal digits in binary representation of n.
%C A336962 This sequence is a permutation of the nonnegative integers, with inverse A336963.
%H A336962 Rémy Sigrist, <a href="/A336962/b336962.txt">Table of n, a(n) for n = 0..8191</a>
%H A336962 Rémy Sigrist, <a href="/A336962/a336962.png">Colored scatterplot of the first 2^16 terms</a> (where the color is function of A136480(n))
%H A336962 <a href="/index/Bi#binary">Index entries for sequences related to binary expansion of n</a>
%H A336962 <a href="/index/Per#IntegerPermutation">Index entries for sequences that are permutations of the natural numbers</a>
%F A336962 a(n) = n iff n = 0 or n belongs to A140690.
%e A336962 The first terms, in decimal and in binary, are:
%e A336962   n   a(n)  bin(n)  bin(a(n))
%e A336962   --  ----  ------  ---------
%e A336962    0     0       0          0
%e A336962    1     1       1          1
%e A336962    2     2      10         10
%e A336962    3     3      11         11
%e A336962    4     6     100        110
%e A336962    5     5     101        101
%e A336962    6     4     110        100
%e A336962    7     7     111        111
%e A336962    8    14    1000       1110
%e A336962    9    11    1001       1011
%e A336962   10    10    1010       1010
%e A336962   11    13    1011       1101
%e A336962   12    12    1100       1100
%e A336962   13     9    1101       1001
%e A336962   14     8    1110       1000
%e A336962   15    15    1111       1111
%o A336962 (PARI) toruns(n) = { my (r=[]); while (n, my (v=valuation(n+n%2,2)); n\=2^v; r=concat(v,r)); r }
%o A336962 fromruns(r) = { my (v=0); for (k=1, #r, v=(v+k%2)*2^r[k]-k%2); v }
%o A336962 a(n) = { my (r=toruns(n)); fromruns(vector(#r, k, r[1+(k-2)%#r])) }
%Y A336962 Cf. A038572, A101211, A136480, A140690, A336963 (inverse).
%K A336962 nonn,base
%O A336962 0,3
%A A336962 _Rémy Sigrist_, Aug 09 2020