A132141 Numbers whose ternary representation begins with 1.
1, 3, 4, 5, 9, 10, 11, 12, 13, 14, 15, 16, 17, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 48, 49, 50, 51, 52, 53, 81, 82, 83, 84, 85, 86, 87, 88, 89, 90, 91, 92, 93, 94, 95, 96, 97, 98, 99, 100, 101, 102, 103, 104, 105, 106, 107, 108
Offset: 1
Links
- Reinhard Zumkeller, Table of n, a(n) for n = 1..10000
- Bryan Brown, Michael Dairyko, Stephan Ramon Garcia, Bob Lutz and Michael Someck, Four quotient set gems, The American Mathematical Monthly, Vol. 121, No. 7 (2014), pp. 590-598; arXiv preprint, arXiv:1312.1036 [math.NT], 2013.
- Christian Mauduit, Propriétés arithmétiques des substitutions, in Séminaire de Théorie des Nombres, Paris, 1989-90, pp. 177-190 (in French).
- Index entries for 3-automatic sequences.
Programs
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Haskell
a132141 n = a132141_list !! (n-1) a132141_list = filter ((== 1) . until (< 3) (flip div 3)) [1..] -- Reinhard Zumkeller, Feb 06 2015
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Mathematica
Flatten[(Range[3^#,2 3^#-1])&/@Range[0,4]] (* Zak Seidov, Mar 03 2009 *)
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PARI
s=[];for(n=0,4,for(x=3^n,2*3^n-1,s=concat(s,x)));s \\ Zak Seidov, Mar 03 2009
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PARI
a(n) = n + 3^logint(n<<1,3) >> 1; \\ Kevin Ryde, Feb 19 2022
Formula
A number n is a term iff 3^m <= n < 2*3^m -1, for m=0,1,2,... - Zak Seidov, Mar 03 2009
a(n) = n + (3^floor(log_3(2*n)) - 1)/2. - Kevin Ryde, Feb 19 2022
Comments