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

1,2

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

Links

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

Example

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

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

Prog

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

Crossrefs

Cf. A032911, A070939.

Sequence in context: A194948 A266679 A285257 * A191211 A263133 A346592

Adjacent sequences: A317404 A317405 A317406 * A317408 A317409 A317410

Keyword

nonn,base

Author

Jeffrey Shallit, Jul 28 2018

Status

approved