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A377836 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(k), r(k-1), ..., r(1)).

%I A377836 #6 Nov 11 2024 08:58:30
%S A377836 0,1,3,2,7,4,15,6,8,5,31,12,16,14,11,63,24,9,32,28,23,127,48,13,30,19,
%T A377836 64,10,56,47,255,17,96,27,60,39,128,20,112,25,95,62,511,35,192,55,22,
%U A377836 120,79,29,256,33,40,224,51,191,124,1023,18,71,384,111,44,240
%N A377836 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(k), r(k-1), ..., r(1)).
%C A377836 This sequence is a bijection from the positive integers to the nonnegative integers.
%H A377836 Rémy Sigrist, <a href="/A377836/b377836.txt">Table of n, a(n) for n = 1..10000</a>
%H A377836 Rémy Sigrist, <a href="/A377836/a377836.gp.txt">PARI program</a>
%H A377836 <a href="/index/Per#IntegerPermutation">Index entries for sequences that are permutations of the natural numbers</a>
%F A377836 A005811(a(n)) = A124830(n).
%F A377836 a(n) = A056539(A377834(n)).
%e A377836 For n = 15: A055932(15) = 60 = 2^2 * 3^1 * 5^1, so the run lengths of the binary expansion of a(15) are (1, 1, 2), the binary expansion of a(15) is "1011", and a(15) = 11.
%o A377836 (PARI) \\ See Links section.
%Y A377836 See A377834 for a similar sequence.
%Y A377836 Cf. A005811, A055932, A124830, A377837 (inverse).
%K A377836 nonn,base
%O A377836 1,3
%A A377836 _Rémy Sigrist_, Nov 09 2024