%I
%S 0,1,1,2,2,3,5,8,6,11,17,28,24,31,55,86,98,135,233,368,256,369,625,
%T 994,1122,1555,2677,4232,3206,5835,9041,14876,12760,16471,29231,45702,
%U 52082,71743,123825,195568,136048,204071,340119,544190,612214,850297,1462511
%N a(n) = a(n2) + A000265(a(n1)), a(0)=0, a(1)=1.
%C The sequence is clearly not monotonic, but the subsequences with even resp. odd indices are both strictly increasing. The sequence is obviously bounded above by the Fibonacci sequence A000045. The subsequence of nth terms, where n is congruent to 2 or 3 mod 4, is bounded below by the Fibonacci sequence; therefore a(2n)>f(n) for n>1.  Joseph Pedersen (jmp456(AT)psu.edu), Feb 27 2006, rephrased by _M. F. Hasler_, Feb 18 2013
%e The highest odd integer dividing a(11)=28 is 7. So a(12) = a(10) + 7 = 17 + 7 = 24.
%e The greatest odd divisor of a(11)=28 is 7, so a(12)= a(10)+7 = 17+7 = 24.
%o (PARI) A114990(n,print_all=0,a=1,o=0)={na=o;for(n=2,n,print_all&print1(a",");a=o+a>>valuation(o=a,2));a} \\ Old versions (<= 2.4) of PARI might require to write o+0+a>>...  _M. F. Hasler_, Feb 18 2013
%Y Cf. A000265.
%K easy,nonn
%O 0,4
%A _Leroy Quet_, Feb 22 2006
%E More terms from Joseph Pedersen (jmp456(AT)psu.edu) and Amy Postell (arp179(AT)psu.edu), Feb 27 2006
%E Edited & initial term a(0)=0 added by _M. F. Hasler_, Feb 18 2013
