

A237568


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).


4



0, 1, 1, 2, 3, 5, 8, 13, 12, 25, 37, 26, 36, 26, 26, 25, 15, 40, 55, 59, 114, 137, 125, 226, 135, 136, 127, 236, 336, 257, 359, 166, 255, 124, 379, 305, 468, 377, 458, 358, 168, 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
(list;
graph;
refs;
listen;
history;
text;
internal format)



OFFSET

0,4


COMMENTS

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.
The sequence is eventually periodic with period of length 144 and the first position of period 237.  Peter J. C. Moses, Feb 09 2014


LINKS

Peter J. C. Moses, Table of n, a(n) for n = 0..952


MATHEMATICA

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 *)


CROSSREFS

Cf. A000045, A001129, A004185, A069638.
Sequence in context: A010077 A065076 A069638 * A272918 A010076 A182444
Adjacent sequences: A237565 A237566 A237567 * A237569 A237570 A237571


KEYWORD

nonn,base


AUTHOR

Vladimir Shevelev, Feb 09 2014


STATUS

approved



