A157971 Odious twin locations: first members of pairs of consecutive odious numbers.

1, 7, 13, 21, 25, 31, 37, 41, 49, 55, 61, 69, 73, 81, 87, 93, 97, 103, 109, 117, 121, 127, 133, 137, 145, 151, 157, 161, 167, 173, 181, 185, 193, 199, 205, 213, 217, 223, 229, 233, 241, 247, 253, 261, 265, 273, 279, 285, 289, 295

Offset

1,2

Comments

An odious number (A000069) is a nonnegative integer with an odd number of ones in its binary expansion.

In the reference it is shown that these odious twins alternate with the evil twins (see A157970), which are pairs of consecutive evil numbers (A001969) having even numbers of ones in their binary expansions.

Links

Amiram Eldar, Table of n, a(n) for n = 1..10000 (terms 1..1000 from Harvey P. Dale)

Chris Bernhardt, Evil twins alternate with odious twins, Math. Mag. 82 (2009), pp. 57-62; also on JSTOR.

Eric Weisstein's World of Mathematics, Odious Number

Example

The sequence of odious numbers (A000069) begins 1,2,4,7,8,11,13,14,16,19,21,..., so the first few odious twins are at 1,7,13, ... .

Mathematica

SequencePosition[Table[If[OddQ[DigitCount[n, 2, 1]], 1, 0], {n, 300}], {1, 1}][[All, 1]] (* Requires Mathematica version 10 or later *) (* Harvey P. Dale, Oct 05 2016 *)

Prog

(PARI) lista(nn) = select(n->((hammingweight(n) % 2) && (hammingweight(n+1) % 2)), vector(nn, i, i)); \\ Michel Marcus, Jul 10 2014

Crossrefs

Cf. A000069, A091855, A157970.

Sequence in context: A109331 A054858 A269704 * A135275 A304005 A304947

Adjacent sequences: A157968 A157969 A157970 * A157972 A157973 A157974

Keyword

nonn

Author

John W. Layman, Mar 10 2009

Extensions

Comment corrected by Jeff Aronson. - N. J. A. Sloane, Oct 04 2020

Status

approved