A361401 -id:A361401 - cp's OEIS frontend

A361379 Distinct values of A361401, in order of appearance.

0, 1, 3, 2, 4, 6, 10, 12, 7, 15, 8, 16, 20, 24, 36, 40, 48, 5, 9, 11, 13, 19, 21, 25, 27, 43, 45, 51, 53, 14, 26, 28, 30, 54, 58, 60, 31, 63, 32, 64, 72, 80, 96, 136, 144, 160, 192, 17, 33, 35, 37, 41, 49, 67, 69, 73, 81, 83, 85, 97, 99, 101, 147, 149, 153

Offset: 0

Rémy Sigrist, Mar 11 2023

This sequence is a permutation of the nonnegative integers with inverse A361422 (for any n >= 0, the value n appears at least in the n-th row of A361401).

			The first rows of A361401, alongside the new values, are:
  n  n-th row of A361401               new values
  -  --------------------------------  -------------------------
  0  0                                 0
  1  1, 3                              1, 3
  2  2, 4, 6, 10, 12                   2, 4, 6, 10, 12
  3  3, 7, 15                          7, 15
  4  4, 8, 12, 16, 20, 24, 36, 40, 48  8, 16, 20, 24, 36, 40, 48
So the present sequence begins with 0, 1, 3, 2, 4, 6, 10, 12, 7, 15, 8, 16, 20, 24, 36, 40, 48.

Rémy Sigrist, Table of n, a(n) for n = 0..9215
Rémy Sigrist, PARI program
Index entries for sequences that are permutations of the natural numbers

Cf. A361401, A361422 (inverse).

PARI
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A361399 a(n) is the least k such that the binary expansion of n is a self-infiltration of that of k.

Original entry on oeis.org

0, 1, 2, 1, 2, 5, 2, 3, 4, 5, 2, 5, 2, 5, 6, 3, 4, 9, 10, 5, 4, 5, 10, 11, 4, 5, 6, 5, 6, 13, 6, 7, 8, 9, 18, 9, 4, 9, 10, 11, 4, 9, 10, 5, 10, 5, 22, 11, 4, 9, 10, 5, 10, 5, 6, 11, 12, 13, 6, 13, 6, 13, 14, 7, 8, 17, 18, 9, 18, 9, 18, 19, 8, 9, 10, 19, 10, 21

Offset: 0

Rémy Sigrist, Mar 10 2023

See A361398 for the definition of an infiltration (a self-infiltration is an infiltration a of word with itself).

a(n) is the index of the first row of A361401 containing n.

Rémy Sigrist, Table of n, a(n) for n = 0..8192
Rémy Sigrist, Colored log-log scatterplot of the first 2^20 terms (the color is function of A070939(a(n)) - A070939(n))
Rémy Sigrist, PARI program
Index entries for sequences related to binary expansion of n

Cf. A020330, A070939, A361398, A361401.

PARI
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See Links section.
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a(n) <= n.

a(A020330(n)) = n.

cp's OEIS Frontend

A361379 Distinct values of A361401, in order of appearance.

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