A157671 Numbers whose ternary representation begins with 2.

2, 6, 7, 8, 18, 19, 20, 21, 22, 23, 24, 25, 26, 54, 55, 56, 57, 58, 59, 60, 61, 62, 63, 64, 65, 66, 67, 68, 69, 70, 71, 72, 73, 74, 75, 76, 77, 78, 79, 80, 162, 163, 164, 165, 166, 167, 168, 169, 170, 171, 172, 173, 174, 175, 176, 177, 178, 179, 180, 181, 182, 183, 184

Offset: 1

Author

Zak Seidov, Mar 04 2009

Keywords

• base
• nonn

Comments

From R. J. Mathar, Mar 03 2009: (Start)

If we look at the sequence first differences, i.e.,

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)

The lower and upper asymptotic densities of this sequence are 1/4 and 1/2, respectively. - Amiram Eldar, Feb 28 2021

Links

• Reinhard Zumkeller, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A034472, A132141, A171960.

Subsequence of A134026. - Reinhard Zumkeller, Jan 20 2010

Programs

Haskell

a157671 n = a157671_list !! (n-1)
a157671_list = filter ((== 2) . until (< 3) (flip div 3)) [1..]
-- Reinhard Zumkeller, Feb 06 2015

Maple

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

Mathematica

Flatten[(Range[2*3^#,3^(#+1)-1])&/@Range[0,4]]
Select[Range[200],First[IntegerDigits[#,3]]==2&] (* Harvey P. Dale, Oct 16 2012 *)
Table[FromDigits[#,3]&/@(Join[{2},#]&/@Tuples[{0,1,2},n]),{n,0,4}]// Flatten (* Harvey P. Dale, Jan 28 2022 *)

PARI

s=[];for(n=0,4,for(x=3^n,2*3^n-1,s=concat(s,x)));s

Formula

A number k is a term if and only if 2*3^m <= k <= 3^(m+1)-1, for m=0,1,2,...

A171960(a(n)) < a(n). - Reinhard Zumkeller, Jan 20 2010