



1, 2, 3, 5, 6, 7, 8, 10, 11, 12, 14, 15, 16, 17, 19, 20, 21, 22, 24, 25, 26, 28, 29, 30, 31, 33, 34, 35, 37, 38, 39, 40, 42, 43, 44, 45, 47, 48, 49, 51, 52, 53, 54, 56, 57, 58, 59, 61, 62, 63, 65, 66, 67, 68, 70, 71, 72, 74, 75, 76, 77, 79, 80, 81, 82, 84
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OFFSET

1,2


COMMENTS

Conjecture: 0 < n*r  a(n) < 1 for n >= 1, where r = (15  sqrt(5))/10. It has been verified by computer that a(n) = floor(n*r) for n=1..3*10^6.
This conjecture can be proved from the result in the Comments of A287769, where it is shown that A287769 is a Sturmian sequence with slope s := 1  1/(3+phi) = (15+sqrt(5))/22. The conjecture then follows from Lemma 9.1.3 in "Automatic sequences", since r = 1/s.  Michel Dekking, Oct 11 2017


REFERENCES

JeanPaul Allouche and Jeffrey Shallit, Automatic sequences, Theory, applications, generalizations, Cambridge University Press, Cambridge, 2003, xvi+571.


LINKS

Clark Kimberling, Table of n, a(n) for n = 1..10000


FORMULA

a(n) = floor(n*r), where r = (15  sqrt(5))/10.  Michel Dekking, Oct 11 2017


MATHEMATICA

s = Nest[Flatten[# /. {0 > {0, 1}, 1 > {0}}] &, {0}, 10] (* A003849 *)
w = StringJoin[Map[ToString, s]]
w1 = StringReplace[w, {"0" > "1", "1" > "110"}]
st = ToCharacterCode[w1]  48 (* A287769 *)
Flatten[Position[st, 0]] (* A276855 *)
Flatten[Position[st, 1]] (* A287770 *)


CROSSREFS

Cf. A276855, A287769.
Sequence in context: A284955 A093480 A121518 * A039080 A093435 A048964
Adjacent sequences: A287767 A287768 A287769 * A287771 A287772 A287773


KEYWORD

nonn,easy


AUTHOR

Clark Kimberling, Jun 03 2017


STATUS

approved



