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A110529
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Numbers n such that n in ternary representation (A007089) has a block of exactly a prime number of consecutive zeros.
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1
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9, 18, 27, 28, 29, 36, 45, 54, 55, 56, 63, 72, 82, 83, 84, 85, 86, 87, 88, 89, 90, 99, 108, 109, 110, 117, 126, 135, 136, 137, 144, 153, 163, 164, 165, 166, 167, 168, 169, 170, 171, 180, 189, 190, 191, 198, 207, 216, 217, 218, 225, 234, 243, 246, 247, 248, 249
(list; graph; refs; listen; history; internal format)
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OFFSET
| 1,1
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COMMENTS
| Related to the Baum-Sweet sequence, but ternary rather than binary and prime rather than odd.
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REFERENCES
| J.-P. Allouche and J. Shallit, Automatic Sequences, Cambridge Univ. Press, 2003, p. 157.
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LINKS
| J.-P. Allouche, Finite Automata and Arithmetic.
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FORMULA
| a(n) is in this sequence iff n (base 3) = A007089(n) has a block (not a sub-block) of a prime number (A000040) of consecutive zeros.
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EXAMPLE
| a(1) = 9 because 9 (base 3) = 100, which has a block of 2 zeros.
a(2) = 18 because 18 (base 3) = 200, which has a block of 2 zeros.
a(3) = 27 because 27 (base 3) = 1000, which has a block of 3 zeros.
81 is not in this sequence because 81 (base 3) = 10000 has a block of 4 consecutive zeros and it does not matter that this has sub-blocks with 2 or 3 consecutive zeros because sub-blocks do not count here.
243 is in this sequence because 243 (base 3) = 100000, which has a block of 5 zeros.
252 is in this sequence because 252 (base 3) = 100100 which has two blocks of 2 consecutive zeros, but we do not require there to be only one such prime-zeros block.
2187 is in this sequence because 2187 (base 3) = 10000000, which has a block of 7 zeros.
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MATHEMATICA
| Select[Range[250], Or @@ (First[ # ] == 0 && PrimeQ[Length[ # ]] &) /@ Split[IntegerDigits[ #, 3]] &] - Ray Chandler (rayjchandler(AT)sbcglobal.net), Sep 12 2005
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CROSSREFS
| Cf. A007089, A037011, A086747, A110471, A110472, A110474.
Sequence in context: A102042 A121282 A205716 * A127887 A037337 A119310
Adjacent sequences: A110526 A110527 A110528 * A110530 A110531 A110532
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KEYWORD
| base,easy,nonn
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AUTHOR
| Jonathan Vos Post (jvospost3(AT)gmail.com), Sep 11 2005
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