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

1, 2, 3, 5, 7, 10, 11, 14, 15, 21, 23, 29, 31, 42, 43, 46, 47, 58, 59, 62, 63, 85, 87, 93, 95, 117, 119, 125, 127, 170, 171, 174, 175, 186, 187, 190, 191, 234, 235, 238, 239, 250, 251, 254, 255, 341, 343, 349, 351, 373, 375, 381, 383, 469, 471, 477, 479, 501

Offset: 1

Author

Jeffrey Shallit, Jul 28 2018

Keywords

• nonn
• base

Comments

Here we number positions starting with the most significant digit as position 1, and continue to the right down to the least significant digit.

From David A. Corneth, Jul 29 2018: (Start)

1 is in the sequence.

If k is in the sequence then so is 2k+1.

(End)

If A070939(k) is odd and k is in the sequence then so is 2*k. - Robert Israel, Jul 31 2018

Examples

			23 is in the sequence because its binary representation is 10111, and it has ones in positions 1,3,5.
		

Links

• Robert Israel, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A032911, A070939.

Programs

Maple

S[1]:= [1]:
for n from 2 to 10 do
  if n::odd then S[n]:= map(t -> 2*t+1, S[n-1])
  else S[n]:= map(t -> (2*t,2*t+1),S[n-1])
  fi
od;
map(op,[seq(S[i],i=1..10)]); # Robert Israel, Jul 31 2018

PARI

isok(n) = {my(b=binary(n)); forstep (i=1, #b, 2, if (!b[i], return (0));); return (1);} \\ Michel Marcus, Jul 29 2018