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A337304 a(n) is the greatest number m not yet in the sequence such that the binary expansions of n and of m have the same runs of consecutive equal digits (up to order but with multiplicity).

%I A337304 #18 Aug 25 2020 22:46:18
%S A337304 0,1,2,3,4,5,6,7,8,9,10,13,12,11,14,15,16,17,20,25,18,21,26,29,24,19,
%T A337304 22,27,28,23,30,31,32,33,40,49,36,41,52,57,34,37,42,53,50,45,58,61,48,
%U A337304 35,44,51,38,43,54,59,56,39,46,55,60,47,62,63,64,65,80,97
%N A337304 a(n) is the greatest number m not yet in the sequence such that the binary expansions of n and of m have the same runs of consecutive equal digits (up to order but with multiplicity).
%C A337304 This sequence has similarities with A337242; here we consider runs, there run lengths.
%C A337304 This sequence is a self-inverse permutation of the nonnegative integers.
%C A337304 This sequence preserves the Hamming weight (A000120), the number of binary digits (A070939) and the number of runs in binary expansions (A005811).
%H A337304 Rémy Sigrist, <a href="/A337304/b337304.txt">Table of n, a(n) for n = 0..8192</a>
%H A337304 Rémy Sigrist, <a href="/A337304/a337304.gp.txt">PARI program for A337304</a>
%H A337304 <a href="/index/Bi#binary">Index entries for sequences related to binary expansion of n</a>
%H A337304 <a href="/index/Per#IntegerPermutation">Index entries for sequences that are permutations of the natural numbers</a>
%F A337304 a(2^k) = 2^k for any k >= 0.
%F A337304 a(2^k-1) = 2^k-1 for any k >= 0.
%e A337304 For n = 303:
%e A337304 - the binary expansion of 43 is "100101111",
%e A337304 - the corresponding runs of consecutive equals digits are "1", "00", "1", "0", "1111",
%e A337304 - there are six numbers k with the same multiset of runs:
%e A337304     k    bin(k)
%e A337304     ---  -----------
%e A337304     303  "100101111"
%e A337304     317  "100111101"
%e A337304     335  "101001111"
%e A337304     377  "101111001"
%e A337304     485  "111100101"
%e A337304     489  "111101001"
%e A337304 - so a(303) = 489,
%e A337304      a(317) = 485,
%e A337304      a(335) = 377,
%e A337304      a(377) = 335,
%e A337304      a(485) = 317,
%e A337304      a(489) = 303.
%o A337304 (PARI) See Links section.
%Y A337304 Cf. A000120, A005811, A070939, A337242.
%K A337304 nonn,look,base
%O A337304 0,3
%A A337304 _Rémy Sigrist_, Aug 22 2020