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A237568 Fibonacci-like 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(n-1) <+> a(n-2). 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[n-1]+a[n-2]]]]; 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

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Last modified November 27 06:44 EST 2022. Contains 358362 sequences. (Running on oeis4.)