A377834 - OEIS

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)).

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, 126, 10, 56, 61, 255, 17, 124, 27, 48, 57, 254, 26, 120, 19, 125, 32, 511, 49, 252, 59, 18, 112, 121, 23, 510, 33, 58, 248, 51, 253, 96, 1023, 22, 113, 508, 123, 50

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OFFSET

1,3

COMMENTS

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

LINKS

Rémy Sigrist, Table of n, a(n) for n = 1..10000

Rémy Sigrist, PARI program

Index entries for sequences that are permutations of the natural numbers

FORMULA

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

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

EXAMPLE

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.

PROG

(PARI) \\ See Links section.

CROSSREFS

See A377836 for a similar sequence.

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

Sequence in context: A252756 A243071 A332811 * A286556 A243354 A362558

Adjacent sequences: A377831 A377832 A377833 * A377835 A377836 A377837

KEYWORD

nonn,base

AUTHOR

Rémy Sigrist, Nov 09 2024

STATUS

approved