

A175326


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


3



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
(list;
graph;
refs;
listen;
history;
text;
internal format)



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



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



KEYWORD

base,nonn


AUTHOR



EXTENSIONS



STATUS

approved



