OFFSET
0,3
COMMENTS
Nonnegative integers with no decimal digit > 2. Thus nonnegative integers in base 10 whose quadrupling by normal addition or multiplication requires no carry operation. - Rick L. Shepherd, Jun 25 2009
REFERENCES
N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
LINKS
T. D. Noe, Table of n, a(n) for n = 0..10000
The Unicode Consortium, Tai Xuan Jing Symbols
Eric Weisstein's World of Mathematics, Ternary.
Wikipedia, Ternary numeral system
R. G. Wilson, V, Letter to N. J. A. Sloane, Sep. 1992
FORMULA
a(0)=0, a(n) = 10*a(n/3) if n==0 (mod 3), a(n) = a(n-1) + 1 otherwise. - Benoit Cloitre, Dec 22 2002
a(n) = 10*a(floor(n/3)) + (n mod 3) if n > 0, a(0) = 0. - M. F. Hasler, Feb 15 2023
MAPLE
A007089 := proc(n) option remember;
if n <= 0 then 0
else
if (n mod 3) = 0 then 10*procname(n/3) else procname(n-1) + 1 fi
fi end:
[seq(A007089(n), n=0..729)]; # - N. J. A. Sloane, Mar 09 2019
MATHEMATICA
Table[ FromDigits[ IntegerDigits[n, 3]], {n, 0, 50}]
PROG
(PARI) a(n)=if(n<1, 0, if(n%3, a(n-1)+1, 10*a(n/3)))
(PARI) a(n)=fromdigits(digits(n, 3)) \\ Charles R Greathouse IV, Jan 08 2017
(Haskell)
a007089 0 = 0
a007089 n = 10 * a007089 n' + m where (n', m) = divMod n 3
-- Reinhard Zumkeller, Feb 19 2012
(Python)
def A007089(n):
n, s = divmod(n, 3); t = 1
while n: n, r = divmod(n, 3); t *= 10; s += r*t
return s # M. F. Hasler, Feb 15 2023
CROSSREFS
KEYWORD
base,nonn,easy
AUTHOR
EXTENSIONS
More terms from James A. Sellers, May 01 2000
STATUS
approved