A353649 -id:A353649 - cp's OEIS frontend

A353650 Inverse permutation to A353649.

0, 1, 2, 4, 6, 5, 3, 13, 7, 9, 11, 15, 17, 20, 10, 8, 16, 12, 14, 18, 37, 39, 41, 21, 23, 25, 31, 27, 29, 33, 35, 43, 46, 48, 54, 50, 52, 56, 60, 58, 63, 28, 30, 32, 24, 22, 34, 26, 47, 49, 19, 36, 38, 40, 42, 51, 53, 55, 104, 44, 112, 114, 108, 106, 116, 110

Offset: 0

Rémy Sigrist, May 01 2022

			A353649(7) = 8 so a(8) = 7.

Rémy Sigrist, Table of n, a(n) for n = 0..10000
Rémy Sigrist, PARI program
Index entries for sequences that are permutations of the natural numbers

Cf. A353649.

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A353648 Lexicographically earliest sequence of distinct nonnegative integers such that for any n >= 0, n and a(n) can be added without carries in balanced ternary.

Original entry on oeis.org

0, 2, 1, 5, 6, 3, 4, 17, 15, 14, 18, 16, 19, 23, 9, 8, 11, 7, 10, 12, 51, 50, 53, 13, 44, 45, 42, 41, 47, 43, 46, 54, 48, 49, 56, 52, 55, 57, 69, 68, 71, 27, 26, 29, 24, 25, 30, 28, 32, 33, 21, 20, 35, 22, 31, 36, 34, 37, 149, 153, 152, 155, 150, 151, 156, 154

Offset: 0

Rémy Sigrist, May 01 2022

Two integers can be added without carries in balanced ternary if they have no equal nonzero digit at the same position.

This sequence is a self-inverse permutation of the nonnegative integers with a single fixed point: a(0) = 0.

			The first terms, in decimal and in balanced ternary, are:
  n         |  0   1   2    3    4    5    6     7     8     9    10    11    12
  a(n)      |  0   2   1    5    6    3    4    17    15    14    18    16    19
  bter(n)   |  0   1  1T   10   11  1TT  1T0   1T1   10T   100   101   11T   110
  bter(a(n))|  0  1T   1  1TT  1T0   10   11  1T0T  1TT0  1TTT  1T00  1TT1  1T01

Rémy Sigrist, Table of n, a(n) for n = 0..10000
Wikipedia, Balanced ternary
Index entries for sequences that are permutations of the natural numbers

Cf. A059095, A238757 (binary analog), A353649.

ok(u, v) = { while (u && v, my (uu=[0, +1, -1][1+u%3], vv=[0, +1, -1][1+v%3]); if (abs(uu+vv)>1, return (0)); u=(u-uu)/3; v=(v-vv)/3); 1 }
{ s=0; for (n=0, 65, for (v=0, oo, if (!bittest(s,v) && ok(n,v), print1 (v", "); s+=2^v; break))) }

cp's OEIS Frontend

A353650 Inverse permutation to A353649.

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