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

Author

Reinhard Zumkeller, Feb 17 2003

Keywords

• nonn
• easy

Examples

			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.
		

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).

Crossrefs

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

Programs

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 *)
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 *)

Python

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

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.