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A147991 Sequence S such that 1 is in S and if x is in S, then 3x-1 and 3x+1 are in S. 8
1, 2, 4, 5, 7, 11, 13, 14, 16, 20, 22, 32, 34, 38, 40, 41, 43, 47, 49, 59, 61, 65, 67, 95, 97, 101, 103, 113, 115, 119, 121, 122, 124, 128, 130, 140, 142, 146, 148, 176, 178, 182, 184, 194, 196, 200, 202, 284, 286, 290, 292, 302, 304, 308, 310, 338, 340, 344, 346 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

COMMENTS

Positive numbers that can be written in balanced ternary without a 0 trit. - J. Hufford, Jun 30 2015

LINKS

Robert Israel, Table of n, a(n) for n = 1..10000

Gevorg Hmayakyan, Trig identity for a(n)

FORMULA

a(n) = 3*a(n/2) - 1 if n>=2 is even, 3*a((n-1)/2) + 1 if n is odd, a(0)=0. - Robert Israel, May 05 2014

G.f. g(x) satisfies g(x) = 3*(x+1)*g(x^2) + x/(1+x). - Robert Israel, May 05 2014

Product_{j=0..n-1} cos(3^j) = 2^(-n+1)*Sum_{i=2^(n-1)..2^n-1} cos(a(i)). - Gevorg Hmayakyan, Jan 15 2017

Sum_{i=2^(n-1)..2^n-1} cos(a(i)/3^(n-1)*Pi/2) = 0. - Gevorg Hmayakyan, Jan 15 2017

EXAMPLE

0th generation: 1;

1st generation: 2 4;

2nd generation: 5 7 11 13.

MAPLE

A147991:= proc(n) option remember; if n::even then 3*procname(n/2)-1 else 3*procname((n-1)/2)+1 fi end proc:

A147991(1):= 1:

[seq](A147991(i), i=1..1000); # Robert Israel, May 05 2014

MATHEMATICA

nn=346; s={1}; While[s1=Select[Union[s, 3*s-1, 3*s+1], # <= nn &];  s != s1, s=s1]; s

PROG

(Haskell)

import Data.Set (singleton, insert, deleteFindMin)

a147991 n = a147991_list !! (n-1)

a147991_list = f $ singleton 1 where

   f s = m : (f $ insert (3*m - 1) $ insert (3*m + 1) s')

         where (m, s') = deleteFindMin s

-- Reinhard Zumkeller, Feb 21 2012, Jan 23 2011

CROSSREFS

Sequence in context: A108464 A128815 A056527 * A033160 A110924 A192590

Adjacent sequences:  A147988 A147989 A147990 * A147992 A147993 A147994

KEYWORD

nonn

AUTHOR

Clark Kimberling, Dec 07 2008

STATUS

approved

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Last modified June 28 09:49 EDT 2017. Contains 288813 sequences.