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

1,1

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

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

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 *)

Prog

(PARI) s=[]; for(n=0, 4, for(x=3^n, 2*3^n-1, s=concat(s, x))); s
(Haskell)
a157671 n = a157671_list !! (n-1)
a157671_list = filter ((== 2) . until (< 3) (flip div 3)) [1..]
-- Reinhard Zumkeller, Feb 06 2015

Crossrefs

Cf. A034472, A132141, A171960.

Subsequence of A134026. - Reinhard Zumkeller, Jan 20 2010

Sequence in context: A088225 A165775 A258826 * A196747 A261691 A351088

Adjacent sequences: A157668 A157669 A157670 * A157672 A157673 A157674

Keyword

base,nonn

Author

Zak Seidov, Mar 04 2009

Status

approved