A105672 a(1)=1, then bracketing n with powers of 3 as f(t)=3^t for f(t) < n <= f(t+1), a(n) = f(t+1) - a(n-f(t)).

1, 2, 1, 8, 7, 8, 1, 2, 1, 26, 25, 26, 19, 20, 19, 26, 25, 26, 1, 2, 1, 8, 7, 8, 1, 2, 1, 80, 79, 80, 73, 74, 73, 80, 79, 80, 55, 56, 55, 62, 61, 62, 55, 56, 55, 80, 79, 80, 73, 74, 73, 80, 79, 80, 1, 2, 1, 8, 7, 8, 1, 2, 1, 26, 25, 26, 19, 20, 19, 26, 25, 26, 1, 2, 1, 8, 7, 8, 1, 2, 1

Offset

1,2

Links

Table of n, a(n) for n=1..81.

Formula

a(n+1) = 1 + Sum_{k=1..n} (-1)^k*(2-3*3^valuation(k, 3)).

a(n) = A064235(n) - a(n - A064235(n)/3). - R. J. Mathar, Nov 06 2011

Maple

A105672 := proc(n)
        option remember;
        if n = 1 then
                1;
        else
                fn1 := A064235(n) ;
                fn := fn1/3 ;
                fn1-procname(n-fn) ;
        end if;
end proc:
seq(A105672(n), n=1..80) ; # R. J. Mathar, Nov 06 2011

Mathematica

A064235[n_] := 3^Ceiling[Log[3, n]]; a[1] = 1; a[n_] := a[n] = A064235[n] - a[n - A064235[n]/3]; Table[a[n], {n, 1, 81}] (* Jean-François Alcover, Jul 09 2013, after R. J. Mathar *)

Prog

(PARI) b(n, m)=if(n<2, 1, m*m^logint(n-1, m)-b(n-m^logint(n-1, m), m))
a(n)=b(n, 3)

Crossrefs

Cf. A105669, A105670, A093347, A093348.

Sequence in context: A254180 A248052 A340629 * A338249 A214271 A372474

Adjacent sequences: A105669 A105670 A105671 * A105673 A105674 A105675

Keyword

nonn

Author

Benoit Cloitre, May 03 2005

Status

approved