A379175 -id:A379175 - cp's OEIS frontend

A379176 Inverse permutation to A379175.

0, 1, 2, 4, 3, 5, 9, 7, 6, 8, 10, 18, 16, 19, 14, 12, 11, 13, 15, 20, 17, 21, 39, 35, 33, 36, 40, 29, 27, 30, 25, 23, 22, 24, 26, 31, 28, 32, 41, 37, 34, 38, 42, 78, 74, 79, 70, 66, 64, 67, 71, 80, 75, 81, 60, 56, 54, 57, 61, 50, 48, 51, 46, 44, 43, 45, 47, 52

Offset: 0

Rémy Sigrist, Dec 17 2024

			A379175(67) = 49, so a(49) = 67.

Rémy Sigrist, Table of n, a(n) for n = 0..10922
Rémy Sigrist, PARI program
Index entries for sequences that are permutations of the natural numbers

Cf. A379175.

PARI
```
\\ See Links section.
```

A379147 Irregular triangle T(n, k), n >= 0, k = 1..2^A007895(n), read by rows; the n-th row lists the integers m such that A184617(abs(m)) = A003714(n).

Original entry on oeis.org

0, -1, 1, -2, 2, -4, 4, -5, -3, 3, 5, -8, 8, -9, -7, 7, 9, -10, -6, 6, 10, -16, 16, -17, -15, 15, 17, -18, -14, 14, 18, -20, -12, 12, 20, -21, -19, -13, -11, 11, 13, 19, 21, -32, 32, -33, -31, 31, 33, -34, -30, 30, 34, -36, -28, 28, 36

Offset: 0

Rémy Sigrist, Dec 16 2024

A permutation of the integers (Z).
For any n >= 0:
- in the Zeckendorf expansion of n,
- replace each Fibonacci number, say A000045(2+i) with i >= 0, by 2^i or -2^i,
- the various values obtained make up the n-th row.

			Triangle T(n, k) begins:
  n   n-th row
  --  ----------------------------------
   0  0
   1  -1, 1
   2  -2, 2
   3  -4, 4
   4  -5, -3, 3, 5
   5  -8, 8
   6  -9, -7, 7, 9
   7  -10, -6, 6, 10
   8  -16, 16
   9  -17, -15, 15, 17
  10  -18, -14, 14, 18
  11  -20, -12, 12, 20
  12  -21, -19, -13, -11, 11, 13, 19, 21
  13  -32, 32
  14  -33, -31, 31, 33
  15  -34, -30, 30, 34

Rémy Sigrist, Table of n, a(n) for n = 0..10922 (rows for n = 0..609 flattened)
Index entries for sequences related to Zeckendorf expansion of n

Cf. A000045, A003714, A007895, A184617, A379175.

tozeck(n) = { for (i=0, oo, if (n<=fibonacci(2+i), my (v=0, f); forstep (j=i, 0, -1, if (n>=f=fibonacci(2+j), n-=f; v+=2^j;); if (n==0, return (v););););); }
row(n) = { my (z = tozeck(n), r = [0], b); while (z, z -= b = 2^valuation(z, 2); r = concat([v - b | v <- r], [v + b | v <- r]);); return (r); }

T(n, 1) = -A003714(n).
T(n, 2^A007895(n)) = A003714(n).
T(n, k) = -T(n, 2^A007895(n)+1-k) for k = 1..2^A007895(n).

cp's OEIS Frontend

A379176 Inverse permutation to A379175.

Views

Author

Keywords

Examples

Links

Crossrefs

Programs

PARI