%I
%S 0,1,1,2,3,5,8,13,12,25,37,26,36,26,26,25,15,40,55,59,114,137,125,226,
%T 135,136,127,236,336,257,359,166,255,124,379,305,468,377,458,358,168,
%U 256,244,500,447,479,269,478,477,559,1036,1559,2559,1148,3707,4558,2568,1267,3358,2456,1458,1349,2708,4057,5667,2479,1468,3479,4479,5789,10268,15067,23355,22348
%N Fibonaccilike sequence of numbers with nondecreasing positive digits. Let a^+ denote the number that is obtained from a if its positive digits are written in nondecreasing order, while zeros remain in their places. Let a<+>b = (a + b)^+. a(0)=0, a(1)=1, for n>=2, a(n) = a(n1) <+> a(n2).
%C Note that operation n^+ differs from the one in A004185. If a term of the sequence has k digits, then it is followed by terms with >=k digits. The sequence has 7 terms with 1 digit, 13 terms with 2 digits, 30 terms with 3 digits, etc. The corresponding maximal terms are 8, 59, 559, etc.
%C The sequence is eventually periodic with period of length 144 and the first position of period 237.  _Peter J. C. Moses_, Feb 09 2014
%H Peter J. C. Moses, <a href="/A237568/b237568.txt">Table of n, a(n) for n = 0..952</a>
%t a[0]:=0;a[1]:=1;a[n_]:=a[n]=FromDigits[Insert[DeleteCases[Sort[#],0],0,1+#Range[Length[#]]&[Position[#,0]]]&[IntegerDigits[a[n1]+a[n2]]]]; Map[a,Range[0,99]] (* _Peter J. C. Moses_, Feb 09 2014 *)
%Y Cf. A000045, A001129, A004185, A069638.
%K nonn,base
%O 0,4
%A _Vladimir Shevelev_, Feb 09 2014
