login
This site is supported by donations to The OEIS Foundation.

 

Logo

Annual Appeal: Please make a donation (tax deductible in USA) to keep the OEIS running. Over 5000 articles have referenced us, often saying "we discovered this result with the help of the OEIS".

Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A110529 Numbers n such that n in ternary representation (A007089) has a block of exactly a prime number of consecutive zeros. 1

%I

%S 9,18,27,28,29,36,45,54,55,56,63,72,82,83,84,85,86,87,88,89,90,99,108,

%T 109,110,117,126,135,136,137,144,153,163,164,165,166,167,168,169,170,

%U 171,180,189,190,191,198,207,216,217,218,225,234,243,246,247,248,249

%N Numbers n such that n in ternary representation (A007089) has a block of exactly a prime number of consecutive zeros.

%C Related to the Baum-Sweet sequence, but ternary rather than binary and prime rather than odd.

%D J.-P. Allouche and J. Shallit, Automatic Sequences, Cambridge Univ. Press, 2003, p. 157.

%H J.-P. Allouche, <a href="http://www.mat.univie.ac.at/~slc/s/s30allouche.html">Finite Automata and Arithmetic</a>, Séminaire Lotharingien de Combinatoire, B30c (1993), 23 pp.

%F 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.

%e a(1) = 9 because 9 (base 3) = 100, which has a block of 2 zeros.

%e a(2) = 18 because 18 (base 3) = 200, which has a block of 2 zeros.

%e a(3) = 27 because 27 (base 3) = 1000, which has a block of 3 zeros.

%e 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.

%e 243 is in this sequence because 243 (base 3) = 100000, which has a block of 5 zeros.

%e 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.

%e 2187 is in this sequence because 2187 (base 3) = 10000000, which has a block of 7 zeros.

%t Select[Range[250], Or @@ (First[ # ] == 0 && PrimeQ[Length[ # ]] &) /@ Split[IntegerDigits[ #, 3]] &] (* _Ray Chandler_, Sep 12 2005 *)

%Y Cf. A007089, A037011, A086747, A110471, A110472, A110474.

%K base,easy,nonn,changed

%O 1,1

%A _Jonathan Vos Post_, Sep 11 2005

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recent | More pages
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy .

Last modified December 10 21:23 EST 2016. Contains 279011 sequences.