A361398 -id:A361398 - cp's OEIS frontend

A361401 Irregular table T(n, k), n >= 0, k = 1..A361398(n); the n-th row lists the numbers whose binary expansion is a self-infiltration of that of n.

0, 1, 3, 2, 4, 6, 10, 12, 3, 7, 15, 4, 8, 12, 16, 20, 24, 36, 40, 48, 5, 9, 11, 13, 19, 21, 25, 27, 43, 45, 51, 53, 6, 12, 14, 26, 28, 30, 54, 58, 60, 7, 15, 31, 63, 8, 16, 24, 32, 40, 48, 64, 72, 80, 96, 136, 144, 160, 192

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).

The terms of the n-th row of A358893 appear in the n-th row of the present table (they correspond to terms with twice as many binary digits as n).

			Table T(n, k) begins:
  n  n-th row
  -  ---------------------------------------------------------
  0  0
  1  1, 3
  2  2, 4, 6, 10, 12
  3  3, 7, 15
  4  4, 8, 12, 16, 20, 24, 36, 40, 48
  5  5, 9, 11, 13, 19, 21, 25, 27, 43, 45, 51, 53
  6  6, 12, 14, 26, 28, 30, 54, 58, 60
  7  7, 15, 31, 63
  8  8, 16, 24, 32, 40, 48, 64, 72, 80, 96, 136, 144, 160, 192

Rémy Sigrist, Table of n, a(n) for n = 0..10102 (rows for n = 0..82 flattened)
Rémy Sigrist, PARI program
Index entries for sequences related to binary expansion of n

Cf. A330941, A358893, A361398.

PARI
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See Links section.
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T(n, 1) = 1.

T(n, A361398(n)) = A330941(n).

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

a(A020330(n)) = n.

cp's OEIS Frontend

A361401 Irregular table T(n, k), n >= 0, k = 1..A361398(n); the n-th row lists the numbers whose binary expansion is a self-infiltration of that of n.

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