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A377834 a(1) = 0, and for n > 0, if A055932(n) = 2^r(1) * 3^r(2) * ... * prime(k)^r(k) with r(k) > 0 (where prime(k) denotes the k-th prime number), then the run lengths of the binary expansion of a(n) are (r(1), r(2), ..., r(k)).

%I A377834 #7 Nov 11 2024 08:58:47
%S A377834 0,1,3,2,7,6,15,4,14,5,31,12,30,8,13,63,28,9,62,24,29,127,60,11,16,25,
%T A377834 126,10,56,61,255,17,124,27,48,57,254,26,120,19,125,32,511,49,252,59,
%U A377834 18,112,121,23,510,33,58,248,51,253,96,1023,22,113,508,123,50
%N A377834 a(1) = 0, and for n > 0, if A055932(n) = 2^r(1) * 3^r(2) * ... * prime(k)^r(k) with r(k) > 0 (where prime(k) denotes the k-th prime number), then the run lengths of the binary expansion of a(n) are (r(1), r(2), ..., r(k)).
%C A377834 This sequence is a bijection from the positive integers to the nonnegative integers.
%H A377834 Rémy Sigrist, <a href="/A377834/b377834.txt">Table of n, a(n) for n = 1..10000</a>
%H A377834 Rémy Sigrist, <a href="/A377834/a377834.gp.txt">PARI program</a>
%H A377834 <a href="/index/Per#IntegerPermutation">Index entries for sequences that are permutations of the natural numbers</a>
%F A377834 A005811(a(n)) = A124830(n).
%F A377834 a(n) = A056539(A377836(n)).
%e A377834 For n = 15: A055932(15) = 60 = 2^2 * 3^1 * 5^1, so the run lengths of the binary expansion of a(15) are (2, 1, 1), the binary expansion of a(15) is "1101", and a(15) = 13.
%o A377834 (PARI) \\ See Links section.
%Y A377834 See A377836 for a similar sequence.
%Y A377834 Cf. A005811, A055932, A124830, A377835 (inverse).
%K A377834 nonn,base
%O A377834 1,3
%A A377834 _Rémy Sigrist_, Nov 09 2024