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

1,2

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.

Links

Lars Blomberg, Table of n, a(n) for n = 1..10000

Lars Blomberg, C# program for generating the b-file

Example

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.

Mathematica

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

Crossrefs

Cf. A175327, A175328.

Sequence in context: A285314 A080544 A178878 * A018676 A115845 A026507

Adjacent sequences: A175323 A175324 A175325 * A175327 A175328 A175329

Keyword

base,nonn

Author

Leroy Quet, Apr 07 2010

Extensions

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

Status

approved