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

Author

Benoit Cloitre, May 03 2005

Keywords

• nonn

Crossrefs

Cf. A105669, A105670, A093347, A093348.

Programs

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 *)

PARI

b(n,m)=if(n<2,1,m*m^floor(log(n-1)/log(m))-b(n-m^floor(log(n-1)/log(m)),m))

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