A321726 Reverse each run of nonzero digits in ternary expansion of n and convert back to decimal.

0, 1, 2, 3, 4, 7, 6, 5, 8, 9, 10, 11, 12, 13, 22, 21, 16, 25, 18, 19, 20, 15, 14, 23, 24, 17, 26, 27, 28, 29, 30, 31, 34, 33, 32, 35, 36, 37, 38, 39, 40, 67, 66, 49, 76, 63, 64, 65, 48, 43, 70, 75, 52, 79, 54, 55, 56, 57, 58, 61, 60, 59, 62, 45, 46, 47, 42, 41

Offset: 0

Author

Rémy Sigrist, Nov 17 2018

Keywords

• nonn
• base
• look

Comments

This sequence is a self-inverse permutation of nonnegative integers.

Examples

			For n = 3497:
- the ternary representation of 3497 is "11210112",
- we replace "1121" by "1211" and "112" by "211" and obtain "12110211",
- hence a(3497) = 3991.
		

Links

• Rémy Sigrist, Table of n, a(n) for n = 0..19683
• Index entries for sequences that are permutations of the natural numbers

Crossrefs

See A321464 for a similar sequence.

Programs

Mathematica

rernz[n_]:=FromDigits[Flatten[If[FreeQ[#,0],Reverse[#],#]&/@SplitBy[ IntegerDigits[ n,3],#!=0&]],3]; Array[rernz,70,0] (* Harvey P. Dale, Nov 15 2020 *)

PARI

a(n, base=3) = my (d=digits(n*base, base), nz=0); for (i=1, #d, if (d[i], nz++, if (nz, for (j=1, floor(nz/2), [d[i-j],d[i-nz-1+j]] = [d[i-nz-1+j],d[i-j]]); nz=0))); fromdigits(d, base)/base

Formula

a(3 * n) = 3 * a(n).