A368229 Irregular table of nonnegative integers T(n, k), n >= 0, k = 1..A001316(n), read by rows: the 1's in the binary expansion of n exactly match the nonzero digits in the ternary expansions of the terms in the n-th row.

0, 1, 2, 3, 6, 4, 5, 7, 8, 9, 18, 10, 11, 19, 20, 12, 15, 21, 24, 13, 14, 16, 17, 22, 23, 25, 26, 27, 54, 28, 29, 55, 56, 30, 33, 57, 60, 31, 32, 34, 35, 58, 59, 61, 62, 36, 45, 63, 72, 37, 38, 46, 47, 64, 65, 73, 74, 39, 42, 48, 51, 66, 69, 75, 78

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 A368230).

Examples

			Table T(n, k) begins:
    0;
    1, 2;
    3, 6;
    4, 5, 7, 8;
    9, 18;
    10, 11, 19, 20;
    12, 15, 21, 24;
    13, 14, 16, 17, 22, 23, 25, 26;
    27, 54;
    28, 29, 55, 56;
    30, 33, 57, 60;
    31, 32, 34, 35, 58, 59, 61, 62;
    36, 45, 63, 72;
    37, 38, 46, 47, 64, 65, 73, 74;
    39, 42, 48, 51, 66, 69, 75, 78;
    40, 41, 43, 44, 49, 50, 52, 53, 67, 68, 70, 71, 76, 77, 79, 80;
    81, 162;
    ...
		

Links

• Rémy Sigrist, Table of n, a(n) for n = 0..6560 (rows for n = 0..2^8-1 flattened)
• Index entries for sequences that are permutations of the natural numbers

Crossrefs

See A368225 for a similar sequence.

Cf. A001316, A005823, A005836, A289831, A368230 (inverse).

Programs

PARI

row(n) = { my (r = [0], b = binary(n)); for (k = 1, #b, r = [3*v+b[k]|v<-r]; if (b[k], r = concat(r, [v+1|v<-r]););); Set(r); }

Formula

T(n, 1) = A005836(n + 1).

T(n, A001316(n)) = A005823(n + 1).

A289831(T(n, k)) = n.