A080544 In binary representation: keep the first digit and rotate right the others twice.

1, 2, 3, 4, 5, 6, 7, 8, 10, 12, 14, 9, 11, 13, 15, 16, 20, 24, 28, 17, 21, 25, 29, 18, 22, 26, 30, 19, 23, 27, 31, 32, 40, 48, 56, 33, 41, 49, 57, 34, 42, 50, 58, 35, 43, 51, 59, 36, 44, 52, 60, 37, 45, 53, 61, 38, 46, 54, 62, 39, 47, 55, 63, 64, 80, 96, 112, 65, 81, 97, 113, 66

Offset: 1

Author

Reinhard Zumkeller, Feb 20 2003

Keywords

• nonn
• base

Comments

a(n) = A080542(A080542(n)); permutation of natural numbers with inverse = A080543: A080543(a(n))=a(A080543(n))=n.

Examples

			a(20)=a('10100')='10001'=17; a(25)=a('11001')='10110'=22.
		

Links

• Ivan Neretin, Table of n, a(n) for n = 1..8192
• Index entries for sequences that are permutations of the natural numbers

Programs

Maple

f:= proc(n) local m,a;
     m:= ilog2(n);
     a:= n mod 4;
     (n - a - 2^m)/4 + 2^(m-2)*a+2^m
end proc:
f(2):= 2:
map(f, [$1..100]); # Robert Israel, Sep 01 2015

Mathematica

Table[FromDigits[Prepend[RotateRight[Rest[IntegerDigits[n, 2]], 2], 1], 2], {n, 72}] (* Ivan Neretin, Aug 30 2015 *)

Formula

a(n) = n - 3*A053645(A002265(n)) + (2^(A000523(n)-2)-1)*A010873(n) for n >= 4. - Robert Israel, Sep 01 2015