|
Search: id:A079734
|
|
|
| A079734 |
|
n for which there is a chain (or permutation) of the numbers from 1 to n for which each adjacent pair sums to a Fibonacci number. |
|
+0
1
|
|
| 2, 3, 4, 5, 7, 8, 9, 11, 12, 13, 20, 21, 33, 34, 54, 55, 88, 89, 143, 144, 232, 233, 376, 377, 609, 610, 986, 987, 1596, 1597, 2583, 2584, 4180, 4181, 6764, 6765, 10945, 10946, 17710, 17711, 28656, 28657, 46367, 46368, 75024, 75025, 121392, 121393
(list; graph; listen)
|
|
|
OFFSET
|
0,1
|
|
|
COMMENT
|
There are no such necklaces (or cycles).
Theorem (Berlekamp & Guy) There exists such a chain just if n = 9 or 11 or F_k or F_k - 1 for k > 3.
|
|
REFERENCES
|
E. R. Berlekamp and R. K. Guy, Paper which MAY be called ``Fibonacci plays Billiards'' and which MAY be submitted to the Monthly.
|
|
EXAMPLE
|
Examples: 1 2; 1 2 3; 4 1 2 3; 4 1 2 3 5; 4 1 7 6 2 3 5; ...
|
|
MAPLE
|
S := {9, 11}: for i from 3 to 50 do S := S union {fibonacci(i)}: S := S union {fibonacci(i)-1}: od: S := S minus {1}: S := convert(S, list): S := sort(S):for i from 1 to nops(S) do printf(`%d, `, S[i]) od:
|
|
CROSSREFS
|
Cf. A079735-A079738.
Sequence in context: A048683 A085233 A133813 this_sequence A050730 A141819 A097904
Adjacent sequences: A079731 A079732 A079733 this_sequence A079735 A079736 A079737
|
|
KEYWORD
|
easy,nonn
|
|
AUTHOR
|
R. K. Guy (rkg(AT)cpsc.ucalgary.ca), Feb 18 2003
|
|
EXTENSIONS
|
More terms and Maple code from James A. Sellers (sellersj(AT)math.psu.edu), Feb 25 2003
|
|
|
Search completed in 0.002 seconds
|
