A175332 - OEIS

%I #17 Feb 26 2022 04:24:43

%S 3,6,7,12,14,15,24,28,30,31,48,56,60,62,63,96,112,120,124,126,127,192,

%T 224,240,248,252,254,255,384,448,480,496,504,508,510,511,768,896,960,

%U 992,1008,1016,1020,1022,1023,1536,1792,1920,1984,2016,2032,2040,2044

%N Numbers whose binary expansion is of the form 11+0*

%C Also numbers n such that the set (2^j)%n consists only of the powers of two.

%H Reinhard Zumkeller, <a href="/A175332/b175332.txt">Table of n, a(n) for n = 1..10000</a>

%H <a href="/index/Bi#binary">Index entries for sequences related to binary expansion of n</a>.

%F Sum_{n>=1} 1/a(n) = -2 + A211705. - _Amiram Eldar_, Feb 26 2022

%o (PARI)

%o is_11p0s(n)=

%o { /* Return whether binary expansion has form 11+0* */

%o   local(b);

%o   if ( n<3, return(0) );

%o   b = binary( n/(2^valuation(n,2) ) );

%o   if ( #b<2, return(0) );

%o   for (j=1,#b, if(b[j]==0, return(0) ) );

%o   return(1);

%o }

%o for (n=1,2100, if (is_11p0s(n), print1(n,", ") ) ); /* show terms */

%o (Haskell)

%o import Data.Set (singleton, deleteFindMin, insert)

%o a175332 n = a175332_list !! (n-1)

%o a175332_list = f $ singleton 3 where

%o   f s = x : f (if even x then insert z s' else insert z $ insert (z+1) s')

%o         where z = 2*x; (x, s') = deleteFindMin s

%o -- _Reinhard Zumkeller_, Sep 24 2014

%o (Python)

%o def a_next(a_n): t = a_n + (a_n & 1); return t | (t >> 1)

%o a_n = 3; a = []

%o for i in range(53): a.append(a_n); a_n = a_next(a_n) # _Falk Hüffner_, Feb 21 2022

%Y Cf. A023758, A007088, A211705.

%K easy,nonn

%O 1,1

%A _Joerg Arndt_, Apr 12 2010