|
Search: id:A060236
|
|
|
| A060236 |
|
If n mod 3 = 0 then a(n)=a(n/3), otherwise a(n)=n mod 3. |
|
+0
6
|
|
| 1, 2, 1, 1, 2, 2, 1, 2, 1, 1, 2, 1, 1, 2, 2, 1, 2, 2, 1, 2, 1, 1, 2, 2, 1, 2, 1, 1, 2, 1, 1, 2, 2, 1, 2, 1, 1, 2, 1, 1, 2, 2, 1, 2, 2, 1, 2, 1, 1, 2, 2, 1, 2, 2, 1, 2, 1, 1, 2, 2, 1, 2, 1, 1, 2, 1, 1, 2, 2, 1, 2, 2, 1, 2, 1, 1, 2, 2, 1, 2, 1, 1, 2, 1, 1, 2, 2, 1, 2, 1, 1, 2, 1, 1, 2, 2, 1, 2, 2, 1, 2, 1, 1, 2, 2
(list; graph; listen)
|
|
|
OFFSET
|
1,2
|
|
|
COMMENT
|
A cube-free word. Start with 1, apply the morphisms 1 -> 121, 2 -> 122, take limit. See A080846 for another version.
Ultimate modulo 3: n-th digit of terms in "Ana sequence" (see A060032 for definition).
Equals A005148(n) reduced mod 3. In "On a sequence Arising in Series for Pi" Morris Newman and Daniel Shanks conjectured that 3 never divides A005148(n) and D. Zagier proved it. - Benoit Cloitre (benoit7848c(AT)orange.fr), Jun 22 2002
Also equals A038502(n) mod 3.
Last nonzero digit in ternary representation of n. - Frank Adams-Watters (FrankTAW(AT)Netscape.net), Apr 01 2006
|
|
REFERENCES
|
J. Berstel and J. Karhumaki, Combinatorics on words - a tutorial, Bull. EATCS, #79 (2003), pp. 178-228.
|
|
LINKS
|
Jean Berstel, Home Page
Index entries for sequences related to final digits of numbers
|
|
EXAMPLE
|
a(10)=1 since 10=3^0*10 and 10 mod 3=1; a(72)=2 since 24=3^3*8 and 8 mod 3=2.
|
|
MATHEMATICA
|
Nest[ Flatten[ # /. {1 -> {1, 2, 1}, 2 -> {1, 2, 2}}] &, {1}, 5] (from Robert G. Wilson v Mar 04 2005)
|
|
PROGRAM
|
(PARI) a(n)=if(n<1, 0, n/3^valuation(n, 3)%3) /* Michael Somos Nov 10 2005 */
|
|
CROSSREFS
|
Cf. A026140 and A026225 for sequence of n's for which a(n)=1, A026179 for sequence of n's for which a(n)=2. k-th term of A060032 is concatenation of first 3^k terms of a(n).
Adjacent sequences: A060233 A060234 A060235 this_sequence A060237 A060238 A060239
Sequence in context: A101566 A051287 A049705 this_sequence A006345 A122497 A023396
|
|
KEYWORD
|
easy,nonn
|
|
AUTHOR
|
Henry Bottomley (se16(AT)btinternet.com), Mar 21 2001
|
|
|
Search completed in 0.002 seconds
|
