A353660 The binary expansions of A352909(n+1, 1) and A352909(n+1, 2) encode respectively the 1's and the 2's in the ternary expansion of a(n).

0, 2, 1, 6, 3, 8, 7, 5, 4, 18, 9, 20, 19, 11, 10, 24, 21, 15, 12, 26, 25, 23, 22, 17, 16, 14, 13, 54, 27, 56, 55, 29, 28, 60, 57, 33, 30, 62, 61, 59, 58, 35, 34, 32, 31, 72, 63, 45, 36, 74, 73, 65, 64, 47, 46, 38, 37, 78, 75, 69, 66, 51, 48, 42, 39, 80, 79, 77

Offset

0,2

Comments

This sequence is a permutation of the nonnegative integers with inverse A353661.

Links

Rémy Sigrist, Table of n, a(n) for n = 0..6560

Index entries for sequences that are permutations of the natural numbers

Formula

a(n) = A005836(A352909(n+1, 1)) + 2*A005836(A352909(n+1, 2)).

a(n) < 3^k iff n < 3^k.

Example

For n = 42:
- A352909(43, 1) = 9,
- A352909(43, 2) = 2,
- the binary expansion of 9 is "1001",
- the binary expansion of 2 is "10",
- so the ternary expansion of a(42) is "1021",
- and a(42) = 34.

Prog

(PARI) b2t(n) = fromdigits(binary(n), 3)
{ n=-1; for (d=0, 2^8-1, for (k=0, d, if (bitand(t1=k, t2=d-k)==0, print1 (b2t(t1) + 2*b2t(t2)", "); if (n++==67, break (2))))) }

Crossrefs

Cf. A005836, A352909, A353661 (inverse), A353662.

Sequence in context: A293182 A124441 A284475 * A285355 A316605 A307178

Adjacent sequences: A353657 A353658 A353659 * A353661 A353662 A353663

Keyword

nonn,look,base

Author

Rémy Sigrist, May 02 2022

Status

approved