A377834 - OEIS

%I #7 Nov 11 2024 08:58:47

%S 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 126,10,56,61,255,17,124,27,48,57,254,26,120,19,125,32,511,49,252,59,

%U 18,112,121,23,510,33,58,248,51,253,96,1023,22,113,508,123,50

%N 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 This sequence is a bijection from the positive integers to the nonnegative integers.

%H Rémy Sigrist, <a href="/A377834/b377834.txt">Table of n, a(n) for n = 1..10000</a>

%H Rémy Sigrist, <a href="/A377834/a377834.gp.txt">PARI program</a>

%H <a href="/index/Per#IntegerPermutation">Index entries for sequences that are permutations of the natural numbers</a>

%F A005811(a(n)) = A124830(n).

%F a(n) = A056539(A377836(n)).

%e 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 (PARI) \\ See Links section.

%Y See A377836 for a similar sequence.

%Y Cf. A005811, A055932, A124830, A377835 (inverse).

%K nonn,base

%O 1,3

%A _Rémy Sigrist_, Nov 09 2024