A368225 Irregular table of nonnegative integers read by rows: the 1's in the binary expansion of n exactly match the nonzero digits in the balanced ternary expansions of the terms in the n-th row.

0, 1, 3, 2, 4, 9, 8, 10, 6, 12, 5, 7, 11, 13, 27, 26, 28, 24, 30, 23, 25, 29, 31, 18, 36, 17, 19, 35, 37, 15, 21, 33, 39, 14, 16, 20, 22, 32, 34, 38, 40, 81, 80, 82, 78, 84, 77, 79, 83, 85, 72, 90, 71, 73, 89, 91, 69, 75, 87, 93, 68, 70, 74, 76, 86, 88, 92, 94

Offset: 0

Author

Rémy Sigrist, Dec 18 2023

Keywords

• nonn
• tabf
• base

Comments

As a flat sequence, this is a permutation of the nonnegative integers with inverse A368226 and infinitely many fixed points (see Formula section).

Row 0 has one term, and for n > 0, row n has A048896(n-1) terms.

For any n >= 0, row n ends with A005836(n+1).

Examples

			Table T(n, k) begins:
    0;
    1;
    3;
    2, 4;
    9;
    8, 10;
    6, 12;
    5, 7, 11, 13;
    27;
    26, 28;
    24, 30;
    23, 25, 29, 31;
    18, 36;
    17, 19, 35, 37;
    15, 21, 33, 39;
    14, 16, 20, 22, 32, 34, 38, 40;
    81;
    ...
		

Links

• Rémy Sigrist, Table of n, a(n) for n = 0..9841 (rows for n = 0..2^9-1 flattened)
• Index entries for sequences that are permutations of the natural numbers

Crossrefs

See A368229 and A368239 for similar sequences.

Cf. A003462, A005836, A048896, A343231, A353662, A368226 (inverse).

Programs

PARI

row(n) = { my (r = [sign(n)], b = binary(n)); for (k = 2, #b, r = [3*v+b[k]|v<-r]; if (b[k], r = concat(r, [v-2|v<-r]););); Set(r); }

Formula

A343231(T(n, k)) = n.

a(m) = m for any m in A003462.