A157970 Evil twin locations: first members of pairs of consecutive evil numbers.

5, 9, 17, 23, 29, 33, 39, 45, 53, 57, 65, 71, 77, 85, 89, 95, 101, 105, 113, 119, 125, 129, 135, 141, 149, 153, 159, 165, 169, 177, 183, 189, 197, 201, 209, 215, 221, 225, 231, 237, 245, 249, 257, 263, 269, 277, 281, 287, 293, 297

Offset

1,1

Comments

An evil number (A001969) is a nonnegative integer with an even number of ones in its binary expansion.

In the reference it is shown that these evil twins alternate with the odious twins (see A157971), which are pairs of consecutive odious numbers (A000069) having an odd number of ones in their binary expansions).

Links

Amiram Eldar, Table of n, a(n) for n = 1..10000

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 evil numbers (A001969) begins 0,3,5,6,9,10,12,15,17,18,20,..., so the first few evil twins are 5, 9, 17, ... .

Mathematica

SequencePosition[Table[If[EvenQ[DigitCount[n, 2, 1]], 1, 0], {n, 300}], {1, 1}][[All, 1]] (* Amiram Eldar, Dec 09 2019 after Harvey P. Dale at A157971 *)

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, A001969, A157971.

Sequence in context: A005006 A369318 A276194 * A054278 A210978 A211434

Adjacent sequences: A157967 A157968 A157969 * A157971 A157972 A157973

Keyword

nonn

Author

John W. Layman, Mar 10 2009

Status

approved