A175326 A positive integer n is included if the run-lengths (of runs both of 0's and of 1's) of the binary representation of n form an arithmetic progression (when written in order).

1, 2, 3, 4, 5, 6, 7, 8, 10, 12, 14, 15, 16, 21, 24, 28, 30, 31, 32, 39, 42, 48, 51, 56, 57, 60, 62, 63, 64, 85, 96, 112, 120, 124, 126, 127, 128, 170, 192, 204, 224, 240, 248, 252, 254, 255, 256, 287, 341, 384, 399, 448, 455, 480, 483, 496, 497, 504

Offset: 1

Author

Leroy Quet, Apr 07 2010

Keywords

• base
• nonn

Comments

The difference between the lengths of consecutive runs in binary n may be either positive, 0, or negative.

This sequence provides a way to order all of the finite sequences each of positive integers arranged in an arithmetic progression (with common difference between consecutive integers being either positive, zero, or negative). See A175327.

Examples

			57 in binary is 111001. The run lengths are therefore 3,2,1, and (3,2,1) forms an arithmetic progression; so 57 is in this sequence.
		

Links

• Lars Blomberg, Table of n, a(n) for n = 1..10000
• Lars Blomberg, C# program for generating the b-file

Crossrefs

Cf. A175327, A175328.

Programs

Mathematica

Select[Range@504, 2 > Length@Union@Differences[Length /@ Split@IntegerDigits[#, 2]] &] (* Giovanni Resta, Feb 15 2013 *)

Extensions

a(30)-a(58) from Lars Blomberg, Feb 15 2013