A377834 -id:A377834 - cp's OEIS frontend

A377835 Inverse of bijection A377834.

1, 2, 4, 3, 8, 10, 6, 5, 14, 18, 28, 24, 12, 15, 9, 7, 25, 32, 47, 40, 68, 83, 59, 50, 20, 26, 38, 34, 17, 21, 13, 11, 42, 52, 75, 65, 108, 129, 94, 81, 150, 179, 227, 213, 132, 157, 116, 99, 35, 44, 63, 55, 91, 111, 79, 69, 29, 36, 53, 46, 23, 30, 19, 16, 67

Offset: 0

Rémy Sigrist, Nov 09 2024

			A377834(42) = 32, so a(32) = 42.

Rémy Sigrist, Table of n, a(n) for n = 0..10000
Rémy Sigrist, PARI program
Index entries for sequences that are permutations of the natural numbers

Cf. A377834.

PARI
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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)).

Original entry on oeis.org

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, 64, 10, 56, 47, 255, 17, 96, 27, 60, 39, 128, 20, 112, 25, 95, 62, 511, 35, 192, 55, 22, 120, 79, 29, 256, 33, 40, 224, 51, 191, 124, 1023, 18, 71, 384, 111, 44, 240

Offset: 1

Rémy Sigrist, Nov 09 2024

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

			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.

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

See A377834 for a similar sequence.

Cf. A005811, A055932, A124830, A377837 (inverse).

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

a(n) = A056539(A377834(n)).

cp's OEIS Frontend

A377835 Inverse of bijection A377834.

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