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A107281
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a(0) = 1, a(1) = 1, a(2) = 2 and for n >= 1: a(n+1) = SORT[a(n) + a(n-1) + a(n-2)] where SORT places digits in ascending order and deletes 0's.
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4
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1, 1, 2, 4, 7, 13, 24, 44, 18, 68, 13, 99, 18, 13, 13, 44, 7, 46, 79, 123, 248, 45, 146, 349, 45, 45, 349, 349, 347, 145, 148, 46, 339, 335, 27, 17, 379, 234, 36, 469, 379, 488, 1336, 223, 247, 168, 368, 378, 149, 589, 1116, 1458, 1336, 139, 2339, 1348, 2368, 556, 2247
(list; graph; refs; listen; history; internal format)
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OFFSET
| 0,3
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COMMENTS
| The maximum value is 56899, which first occurs at a(275). The maximum next occurs at a(977). T. D. Noe (noe(AT)sspectra.com) verified that the terms around a(275) and a(977) are the same. Hence the period is 977 - 275 = 702. The actual period starts at a(24) with the interesting terms 349, 45, 45, 349, 349. For some different initial conditions, the period is different. The point of the SORT operation here is that it "mixes" the sequence and the questions are, considering cycles as orbits, all about ergodicity. To turn this into the sorted Fibonacci sequence (A069638), use a(0)=0, a(1)=1, a(2)=1. This is a "base" sequence, but has analogs in other bases; for instance, SORT(base 2)[n] means count the number of 1's in the binary, call that k and output 2^(k-1). How does this sequence depend on SORT(base M)[n] for various M? Are there any initial values such that the sequence us unbounded? If not, how does cycle length depend upon initial values?
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REFERENCES
| Richard I. Hess, "Problem 920: sorted Fibonacci sequence", Pi Mu Epsilon Journal, Vol. 10 (Fall 1998) No. 9, pp. 754-755.
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FORMULA
| a(0) = 1, a(1) = 1, a(2) = 2 and for n>1: a(n+1) = SORT[a(n) + a(n-1) + a(n-2)] where SORT places digits in ascending order and deletes 0.
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EXAMPLE
| a(8) = 18 because a(5) + a(6) + a(7) = 13 + 24 + 44 = 81 and SORT(81) = 18.
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MATHEMATICA
| nxt[{a_, b_, c_}]:=Module[{d=FromDigits[Sort[IntegerDigits[a+b+c]]]}, {b, c, d}]; Transpose[NestList[nxt, {1, 1, 2}, 65]][[1]] (* From Harvey P. Dale, Feb 07 2011 *)
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CROSSREFS
| Cf. A000073, A069638.
Sequence in context: A049285 A002843 A128742 * A006744 A054175 A000073
Adjacent sequences: A107278 A107279 A107280 * A107282 A107283 A107284
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KEYWORD
| base,easy,nonn
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AUTHOR
| Jonathan Vos Post (jvospost3(AT)gmail.com), Jun 08 2005
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