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

Author

John W. Layman, Mar 10 2009

Keywords

• nonn
• easy

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).

Examples

			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, ... .
		

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.

Crossrefs

Cf. A000069, A001969, A157971, A248056.

Programs

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 *)

PARI

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

Formula

a(n) = A248056(n) - 1. - Amiram Eldar, Jun 16 2025