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

1,2

Comments

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

Links

Ivan Neretin, Table of n, a(n) for n = 1..8192

Index entries for sequences that are permutations of the natural numbers

Formula

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

Example

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

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 *)

Crossrefs

Sequence in context: A270189 A257672 A285314 * A178878 A175326 A018676

Adjacent sequences: A080541 A080542 A080543 * A080545 A080546 A080547

Keyword

nonn,base

Author

Reinhard Zumkeller, Feb 20 2003

Status

approved