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A132141
Numbers whose ternary representation begins with 1.
12
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
1,2
COMMENTS
The lower and upper asymptotic densities of this sequence are 1/2 and 3/4, respectively. - Amiram Eldar, Feb 28 2021
LINKS
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).
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
MATHEMATICA
Flatten[(Range[3^#, 2 3^#-1])&/@Range[0, 4]] (* Zak Seidov, Mar 03 2009 *)
PROG
(PARI) s=[]; for(n=0, 4, for(x=3^n, 2*3^n-1, s=concat(s, x))); s \\ Zak Seidov, Mar 03 2009
(PARI) a(n) = n + 3^logint(n<<1, 3) >> 1; \\ Kevin Ryde, Feb 19 2022
(Haskell)
a132141 n = a132141_list !! (n-1)
a132141_list = filter ((== 1) . until (< 3) (flip div 3)) [1..]
-- Reinhard Zumkeller, Feb 06 2015
CROSSREFS
KEYWORD
nonn,base,easy
AUTHOR
Reinhard Zumkeller, Aug 20 2007
STATUS
approved