A080414 Take the rightmost three binary digits of n (for n<4 padded with leading zeros) and rotate right 1 digit.

0, 4, 1, 5, 2, 6, 3, 7, 8, 12, 9, 13, 10, 14, 11, 15, 16, 20, 17, 21, 18, 22, 19, 23, 24, 28, 25, 29, 26, 30, 27, 31, 32, 36, 33, 37, 34, 38, 35, 39, 40, 44, 41, 45, 42, 46, 43, 47, 48, 52, 49, 53, 50, 54, 51, 55, 56, 60, 57, 61, 58, 62, 59, 63, 64, 68, 65, 69, 66, 70, 67, 71, 72

Offset

0,2

Links

Harvey P. Dale, Table of n, a(n) for n = 0..1000

Index entries for sequences that are permutations of the natural numbers.

Index entries for linear recurrences with constant coefficients, signature (1,0,0,0,0,0,0,1,-1).

Formula

For n>7: a(n) = 8*floor(n/8) + a(n mod 8).

A permutation of natural numbers with inverse A080413: A080413(a(n))=n, a(A080413(n))=n.

a(a(n))=A080413(n), A080413(A080413(n))=a(n), a(a(a(n)))=n.

From Elmo R. Oliveira, May 11 2026: (Start)

a(n) = a(n-1) + a(n-8) - a(n-9).

G.f.: x*(4-3*x+4*x^2-3*x^3+4*x^4-3*x^5+4*x^6+x^7) / ((1+x)*(1+x^2)*(1+x^4)*(x-1)^2). (End)

Example

a(2)=a('010')='001'=1; a(3)=a('011')='101'=5; a(4)=a('100')='010'=2; a(5)=a('101')='110'=6;
a(20)=a('10'100')='10'010'=18; a(21)=a('10'101')='10'110'=22.

Mathematica

r3bd[n_]:=Module[{a, b}, {a, b}=Reverse[TakeDrop[IntegerDigits[n, 2], -3]]; FromDigits[Join[a, RotateRight[b]], 2]]; Join[{0, 4, 1, 5}, Table[r3bd[n], {n, 4, 80}]] (* Harvey P. Dale, Jul 30 2021 *)
(* Alternative: *)
LinearRecurrence[{1, 0, 0, 0, 0, 0, 0, 1, -1}, {0, 4, 1, 5, 2, 6, 3, 7, 8}, 73] (* Georg Fischer, Jul 03 2025 *)

Prog

(Python)
def A080414(n): return ((n&6)>>1)+((n&1)<<2)+(n&-8) # Chai Wah Wu, Jan 21 2023

Crossrefs

Cf. A004442, A007088, A064429, A080412, A080413.

Sequence in context: A076063 A035590 A168230 * A067061 A115210 A199150

Adjacent sequences: A080411 A080412 A080413 * A080415 A080416 A080417

Keyword

nonn,easy

Author

Reinhard Zumkeller, Feb 17 2003

Status

approved