A139709 Take n in binary. Rotate the binary digits to the left until a 1 once again appears as the leftmost digit. a(n) is result written in binary.

1, 10, 11, 100, 110, 101, 111, 1000, 1100, 1010, 1110, 1001, 1011, 1101, 1111, 10000, 11000, 10100, 11100, 10010, 10110, 11010, 11110, 10001, 10011, 10101, 10111, 11001, 11011, 11101, 11111, 100000, 110000, 101000, 111000, 100100, 101100

Offset

1,2

Comments

This sequence written in decimal is A139708.

Links

Michael De Vlieger, Table of n, a(n) for n = 1..10000

Example

For n = 11 (in decimal): 11 (in decimal) = 1011 in binary. Rotate once to the left, getting 0111. The leftmost digit is a 0, so rotate again to the left, getting 1110. A 1 is the leftmost digit, so stop here. a(11) therefore is 1110 (which is 14 in decimal).

Maple

A007088 := proc(L) local i ; add(op(i, L)*10^(i-1), i=1..nops(L)) : end: A139709 := proc(n) local a; a := ListTools[Rotate](convert(n, base, 2), -1) ; while op(-1, a) = 0 do a := ListTools[Rotate](a, -1) ; od: A007088(a) ; end: seq(A139709(n), n=1..80) ; # R. J. Mathar, May 04 2008

Mathematica

Array[FromDigits@ NestWhile[RotateLeft, IntegerDigits[#, 2], First@ # == 0 &, {2, 1}] &, 37] (* Michael De Vlieger, Oct 22 2017 *)

Prog

(PARI) rot(n) = if(#Str(n)==1, v=vector(1), v=vector(#n-1)); for(i=2, #n, v[i-1]=n[i]); u=vector(#n); for(i=1, #n, u[i]=n[i]); v=concat(v, u[1]); v
a(n) = my(b=rot(binary(n))); while(b[1]==0, b=rot(b)); subst(Pol(b), x, 10) \\ Felix Fröhlich, Oct 22 2017

Crossrefs

Cf. A007088, A139707, A139708.

Sequence in context: A043681 A234472 A139707 * A221714 A309761 A108779

Adjacent sequences: A139706 A139707 A139708 * A139710 A139711 A139712

Keyword

nonn,base,easy

Author

Leroy Quet, Apr 30 2008

Extensions

More terms from R. J. Mathar, May 04 2008

Status

approved