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A030102
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Base-3 reversal of n (written in base 10).
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37
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0, 1, 2, 1, 4, 7, 2, 5, 8, 1, 10, 19, 4, 13, 22, 7, 16, 25, 2, 11, 20, 5, 14, 23, 8, 17, 26, 1, 28, 55, 10, 37, 64, 19, 46, 73, 4, 31, 58, 13, 40, 67, 22, 49, 76, 7, 34, 61, 16, 43, 70, 25, 52, 79, 2, 29, 56, 11, 38, 65, 20, 47, 74, 5, 32, 59, 14, 41, 68, 23, 50, 77, 8, 35, 62, 17, 44, 71
(list;
graph;
refs;
listen;
history;
text;
internal format)
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OFFSET
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0,3
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LINKS
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FORMULA
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a(n) = t(n,0) with t(n,r) = if n=0 then r else t(floor(n/3),r*3+(n mod 3)). - Reinhard Zumkeller, Mar 04 2010
G.f. G(x) satisfies: G(x) = (1+x+x^2)*G(x^3) - (1+2*x)*(x + 2*Sum_{m>=0} 3^m*x^(3^(m+1)+1)/(x^3-1). - Robert Israel, Dec 24 2015
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EXAMPLE
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a(17) = 25 because 17 in base 3 is 122, and backwards that is 221, which is 25 in base 10.
a(18) = 2 because 18 in base 3 is 200, and backwards that is 2.
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MAPLE
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a030102:= proc(n) option remember;
local y;
y:= n mod 3;
3^ilog[3](n)*y + procname((n-y)/3)
end proc:
for i from 0 to 2 do a030102(i):= i od:
# alternative
local r ;
r := ListTools[Reverse](convert(n, base, 3)) ;
add(op(i, r)*3^(i-1), i=1..nops(r)) ;
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MATHEMATICA
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FromDigits[#, 3]&/@(Reverse/@IntegerDigits[Range[0, 80], 3]) (* Harvey P. Dale, Feb 05 2020 *)
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PROG
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(PARI) a(n, b=3)=subst(Polrev(base(n, b)), x, b) /* where */
base(n, b)={my(a=[n%b]); while(0<n\=b, a=concat(n%b, a)); a} \\ M. F. Hasler, Nov 04 2011
(PARI) a(n) = fromdigits(Vecrev(digits(n, 3)), 3); \\ Michel Marcus, Oct 10 2017
(Haskell)
a030102 = foldl (\v d -> 3 * v + d) 0 . a030341_row
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CROSSREFS
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Cf. A263273 for a bijective variant.
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KEYWORD
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AUTHOR
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STATUS
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approved
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