A353660 -id:A353660 - cp's OEIS frontend

A353661 Inverse permutation to A353660.

0, 2, 1, 4, 8, 7, 3, 6, 5, 10, 14, 13, 18, 26, 25, 17, 24, 23, 9, 12, 11, 16, 22, 21, 15, 20, 19, 28, 32, 31, 36, 44, 43, 35, 42, 41, 48, 56, 55, 64, 80, 79, 63, 78, 77, 47, 54, 53, 62, 76, 75, 61, 74, 73, 27, 30, 29, 34, 40, 39, 33, 38, 37, 46, 52, 51, 60, 72

Offset: 0

Rémy Sigrist, May 02 2022

			A353660(7) = 5, so a(5) = 7.

Rémy Sigrist, Table of n, a(n) for n = 0..6560
Rémy Sigrist, PARI program
Index entries for sequences that are permutations of the natural numbers

Cf. A353660.

PARI
```
See Links section.
```

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

A353662 The binary expansions of A352909(n+1, 1) and A352909(n+1, 2) encode respectively the 1's and the -1's in the balanced ternary expansion of a(n).

Original entry on oeis.org

0, -1, 1, -3, 3, -4, -2, 2, 4, -9, 9, -10, -8, 8, 10, -12, -6, 6, 12, -13, -11, -7, -5, 5, 7, 11, 13, -27, 27, -28, -26, 26, 28, -30, -24, 24, 30, -31, -29, -25, -23, 23, 25, 29, 31, -36, -18, 18, 36, -37, -35, -19, -17, 17, 19, 35, 37, -39, -33, -21, -15, 15

Offset: 0

Rémy Sigrist, May 02 2022

This sequence is a permutation from the nonnegative integers onto the integers (Z).

			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 balanced ternary expansion of a(42) is "10T1",
- and a(42) = 25.

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

Cf. A005836, A074330, A117966, A352909, A353660.

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) - b2t(t2)", "); if (n++==61, break (2))))) }

a(n) = A005836(A352909(n+1, 1)) - A005836(A352909(n+1, 2)).
a(n) = A117966(A353660(n)).
Sum_{k = 0..n} a(k) = 0 iff n = 0 or n belongs to A074330.

cp's OEIS Frontend

A353661 Inverse permutation to A353660.

Views

Author

Keywords

Examples

Links

Crossrefs

Programs

PARI

Formula