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Search: id:A110471
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| A110471 |
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Prime analogue of Baum-Sweet sequence: a(n) = 1 if binary representation of n contains no block of consecutive zeros of exactly prime length; otherwise a(n) = 0. |
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+0
6
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| 1, 1, 1, 1, 0, 1, 1, 1, 0, 0, 1, 1, 0, 1, 1, 1, 1, 0, 0, 0, 0, 1, 1, 1, 0, 0, 1, 1, 0, 1, 1, 1, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 0, 1, 1, 1, 1, 0, 0, 0, 0, 1, 1, 1, 0, 0, 1, 1, 0, 1, 1, 1, 1, 0, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 1, 1, 1, 0, 0, 1, 1, 0, 1, 1, 1, 0, 1, 0, 0, 0, 0, 0, 0, 0
(list; graph; listen)
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OFFSET
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0,1
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REFERENCES
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J.-P. Allouche and J. Shallit, Automatic Sequences, Cambridge Univ. Press, 2003, p. 157.
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LINKS
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J.-P. Allouche, Finite Automata and Arithmetic.
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EXAMPLE
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a(4) = 0 because 4 (base 2) = 100, which has 2 (prime) consecutive zeros.
a(8) = 0 because 8 (base 2) = 1000, which has 3 (prime) consecutive zeros.
a(9) = 0 because 9 (base 2) = 1001, which has 2 (prime) consecutive zeros.
a(16) = 1 because 16 (base 2) = 10000, which has 4 (composite) consecutive zeros, even though there are sub-blocks of zeros of lengths 2 and 3.
a(32) = 0 because 32 (base 2) = 100000, which has 5 (prime) consecutive zeros.
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MATHEMATICA
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f[n_] := If[Or @@ (First[ # ] == 0 && PrimeQ[Length[ # ]] &) /@ Split[IntegerDigits[n, 2]], 0, 1]; Table[f[n], {n, 0, 120}] (*Chandler*)
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CROSSREFS
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Cf. A037011, A086747, A110472, A110474.
Sequence in context: A115954 A115526 A054524 this_sequence A103994 A051731 A135839
Adjacent sequences: A110468 A110469 A110470 this_sequence A110472 A110473 A110474
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KEYWORD
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base,easy,nonn
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AUTHOR
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Jonathan Vos Post (jvospost3(AT)gmail.com), Sep 07 2005
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EXTENSIONS
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Extended by Ray Chandler (rayjchandler(AT)sbcglobal.net), Sep 16 2005
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