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%I #25 Jan 28 2022 12:16:31
%S 2,6,7,8,18,19,20,21,22,23,24,25,26,54,55,56,57,58,59,60,61,62,63,64,
%T 65,66,67,68,69,70,71,72,73,74,75,76,77,78,79,80,162,163,164,165,166,
%U 167,168,169,170,171,172,173,174,175,176,177,178,179,180,181,182,183,184
%N Numbers whose ternary representation begins with 2.
%C From _R. J. Mathar_, Mar 03 2009: (Start)
%C If we look at the sequence first differences, i.e.,
%C 2, 4, 1, 1, 10, 1, 1, 1, 1, 1, 1, 1, 1, 28, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 82, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, we obtain the records in A034472. (End)
%C The lower and upper asymptotic densities of this sequence are 1/4 and 1/2, respectively. - _Amiram Eldar_, Feb 28 2021
%H Reinhard Zumkeller, <a href="/A157671/b157671.txt">Table of n, a(n) for n = 1..10000</a>
%F A number k is a term if and only if 2*3^m <= k <= 3^(m+1)-1, for m=0,1,2,...
%F A171960(a(n)) < a(n). - _Reinhard Zumkeller_, Jan 20 2010
%p for n from 1 to 300 do dgs := convert(n,base,3) ; if op(-1,dgs) = 2 then printf("%d,",n) ; fi; od: # _R. J. Mathar_, Mar 03 2009
%t Flatten[(Range[2*3^#,3^(#+1)-1])&/@Range[0,4]]
%t Select[Range[200],First[IntegerDigits[#,3]]==2&] (* _Harvey P. Dale_, Oct 16 2012 *)
%t Table[FromDigits[#,3]&/@(Join[{2},#]&/@Tuples[{0,1,2},n]),{n,0,4}]// Flatten (* _Harvey P. Dale_, Jan 28 2022 *)
%o (PARI) s=[];for(n=0,4,for(x=3^n,2*3^n-1,s=concat(s,x)));s
%o (Haskell)
%o a157671 n = a157671_list !! (n-1)
%o a157671_list = filter ((== 2) . until (< 3) (flip div 3)) [1..]
%o -- _Reinhard Zumkeller_, Feb 06 2015
%Y Cf. A034472, A132141, A171960.
%Y Subsequence of A134026. - _Reinhard Zumkeller_, Jan 20 2010
%K base,nonn
%O 1,1
%A _Zak Seidov_, Mar 04 2009
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