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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).
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
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.
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
Sequence in context: A285314 A080544 A178878 * A018676 A115845 A026507
KEYWORD
base,nonn
AUTHOR
Leroy Quet, Apr 07 2010
EXTENSIONS
a(30)-a(58) from Lars Blomberg, Feb 15 2013
STATUS
approved