A368239 Irregular table of nonnegative integers T(n, k), n >= 0, k = 1..A080100(n), read by rows; the 1's in the binary expansion of n exactly match the 1's in the balanced ternary expansions of the terms in the n-th row.

0, 1, 2, 3, 4, 5, 6, 8, 9, 7, 10, 11, 12, 13, 14, 15, 17, 18, 23, 24, 26, 27, 16, 19, 25, 28, 20, 21, 29, 30, 22, 31, 32, 33, 35, 36, 34, 37, 38, 39, 40, 41, 42, 44, 45, 50, 51, 53, 54, 68, 69, 71, 72, 77, 78, 80, 81, 43, 46, 52, 55, 70, 73, 79, 82, 47, 48, 56, 57, 74, 75, 83, 84

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 A368240.

Examples

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

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 A368225 for a similar sequence.

Cf. A005836, A080100, A147991, A343228, A368240 (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]==0, r = concat(r, [v-1|v<-r]););); Set(r); }

Formula

T(n, 1) = A147991(n) for any n > 0.

T(n, A080100(n)) = A005836(n + 1).

A343228(T(n, k)) = n.