A341220 Irregular table read by rows T(n, k), n >= 0, k = 1..A341218(n); T(n, k) is the k-th number m such that A340873(m) = n.

1, 2, 4, 3, 8, 6, 7, 16, 12, 14, 15, 32, 5, 24, 28, 30, 31, 64, 10, 11, 48, 56, 60, 62, 63, 128, 20, 21, 22, 23, 96, 112, 120, 124, 126, 127, 256, 13, 40, 42, 43, 44, 46, 47, 192, 224, 240, 248, 252, 254, 255, 512, 25, 26, 27, 80, 84, 85, 86, 87, 88, 92, 94, 95, 384, 448, 480, 496, 504, 508, 510, 511, 1024

Offset

0,2

Comments

Each positive integer appears once.

For any n >= 0:

- if m appears in row n, then 2*m appears in row n+1,

- if m appears in row n and is an odious even number > 2, then an additional odd number appears in row n+1.

Links

Rémy Sigrist, Table of n, a(n) for n = 0..11792 (rows 0..26)

Rémy Sigrist, PARI program for A341220

Index entries for sequences related to 3x+1 (or Collatz) problem

Index entries for sequences that are permutations of the natural numbers

Formula

T(n, 1) = A341194(n).

T(n, A341218(n)) = 2^n.

Example

Table begins:
    1;
    2;
    4;
    3, 8;
    6, 7, 16;
    12, 14, 15, 32;
    5, 24, 28, 30, 31, 64;
    10, 11, 48, 56, 60, 62, 63, 128;
    20, 21, 22, 23, 96, 112, 120, 124, 126, 127, 256;
    13, 40, 42, 43, 44, 46, 47, 192, 224, 240, 248, 252, 254, 255, 512;
    ...

Prog

(PARI) See Links section.

Crossrefs

Cf. A127824, A340873, A341194, A341218.

Sequence in context: A209636 A243491 A271863 * A253563 A294044 A243072

Adjacent sequences: A341217 A341218 A341219 * A341221 A341222 A341223

Keyword

nonn,look,base,tabf

Author

Rémy Sigrist, Feb 07 2021

Status

approved