cp's OEIS Frontend

A317407 The "OOPS" numbers -- numbers with ones in all odd-numbered positions of the binary representation of n.

%I A317407 #35 Aug 03 2018 11:01:46
%S A317407 1,2,3,5,7,10,11,14,15,21,23,29,31,42,43,46,47,58,59,62,63,85,87,93,
%T A317407 95,117,119,125,127,170,171,174,175,186,187,190,191,234,235,238,239,
%U A317407 250,251,254,255,341,343,349,351,373,375,381,383,469,471,477,479,501
%N A317407 The "OOPS" numbers -- numbers with ones in all odd-numbered positions of the binary representation of n.
%C A317407 Here we number positions starting with the most significant digit as position 1, and continue to the right down to the least significant digit.
%C A317407 From _David A. Corneth_, Jul 29 2018: (Start)
%C A317407 1 is in the sequence.
%C A317407 If k is in the sequence then so is 2k+1.
%C A317407 (End)
%C A317407 If A070939(k) is odd and k is in the sequence then so is 2*k. - _Robert Israel_, Jul 31 2018
%H A317407 Robert Israel, <a href="/A317407/b317407.txt">Table of n, a(n) for n = 1..10000</a>
%e A317407 23 is in the sequence because its binary representation is 10111, and it has ones in positions 1,3,5.
%p A317407 S[1]:= [1]:
%p A317407 for n from 2 to 10 do
%p A317407   if n::odd then S[n]:= map(t -> 2*t+1, S[n-1])
%p A317407   else S[n]:= map(t -> (2*t,2*t+1),S[n-1])
%p A317407   fi
%p A317407 od;
%p A317407 map(op,[seq(S[i],i=1..10)]); # _Robert Israel_, Jul 31 2018
%o A317407 (PARI) isok(n) = {my(b=binary(n)); forstep (i=1, #b, 2, if (!b[i], return (0));); return (1);} \\ _Michel Marcus_, Jul 29 2018
%Y A317407 Cf. A032911, A070939.
%K A317407 nonn,base
%O A317407 1,2
%A A317407 _Jeffrey Shallit_, Jul 28 2018