OFFSET
1,2
COMMENTS
Sequence is a permutation of the positive integers. a(2n-1) is the smallest positive integer not occurring earlier in the sequence.
It seems that A101925 is the odd bisection, A045412 is the sorted even bisection: a(2*n) = A045412(a(n)). - Andrey Zabolotskiy, Oct 09 2019
LINKS
FORMULA
a(2^m) = 2^(m+1) - 1; a(2^m+k) = a(k) + 2^m - 1 for 0 < k < 2^m. - Andrey Zabolotskiy, Oct 10 2019
EXAMPLE
4 is the highest power of 2 dividing 12. Those positive integers not occurring among the first 11 terms of the sequence form the sequence 11, 12, 13, 14, 16,... Now 14 is the 4th of these integers, so a(12) = 14.
MAPLE
A118319 := proc(nmin) local a, anxt, i, n ; a := [1] ; while nops(a) < nmin do n := nops(a)+1 ; i := 2^A007814(n); anxt := 0 ; while i > 0 do anxt := anxt+1 ; while anxt in a do anxt := anxt+1 ; od ; i := i-1; od ; a := [op(a), anxt] ; od; a ; end: A118319(80) ; # R. J. Mathar, Sep 06 2007
MATHEMATICA
a[1] := 1; a[n_] := a[n] = Part[ Complement[ Range[2 n], Table[a[i], {i, n - 1}]], 2^IntegerExponent[n, 2]]; Array[a, 100] (* Birkas Gyorgy, Jul 09 2012 *)
CROSSREFS
KEYWORD
easy,nonn
AUTHOR
Leroy Quet, Apr 23 2006
EXTENSIONS
More terms from R. J. Mathar, Sep 06 2007
STATUS
approved