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Search: id:A090281
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| A090281 |
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"Plain Bob Minimus" in bell-ringing is a sequence of permutations p_1=(1,2,3,4), p_2=(2,1,4,3), .. which runs through all permutations of {1,2,3,4} with period 24; sequence gives position of bell 1 (the treble bell) in n-th permutation. |
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8
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| 1, 2, 3, 4, 4, 3, 2, 1, 1, 2, 3, 4, 4, 3, 2, 1, 1, 2, 3, 4, 4, 3, 2, 1, 1, 2, 3, 4, 4, 3, 2, 1, 1, 2, 3, 4, 4, 3, 2, 1, 1, 2, 3, 4, 4, 3, 2, 1, 1, 2, 3, 4, 4, 3, 2, 1, 1, 2, 3, 4, 4, 3, 2, 1, 1, 2, 3, 4, 4, 3, 2, 1, 1, 2, 3, 4, 4, 3, 2, 1, 1, 2, 3, 4, 4, 3, 2, 1, 1, 2, 3, 4, 4, 3, 2, 1, 1, 2, 3
(list; graph; listen)
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OFFSET
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1,2
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COMMENT
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This is the "plain hunting" sequence with 4 bells.
a(n) is also the position of bell 4 (the tenor bell) in the (n+4)-th permutation of the "Fourth down, Extream between the two farthest Bells from it" bell-ringing permutation, A143484. [From Alois P. Heinz (heinz(AT)hs-heilbronn.de), Aug 19 2008]
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LINKS
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R. Bailey, Change Ringing Resources
David Joyner, Application: Bell Ringing
M.I.T. Bell-Ringers, General Information On Change Ringing
Index entries for sequences related to bell ringing
The Project Gutenberg EBook of Tintinnalogia, or, the Art of Ringing, by Richard Duckworth and Fabian Stedman [From Alois P. Heinz (heinz(AT)hs-heilbronn.de), Aug 19 2008]
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FORMULA
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Period 24.
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EXAMPLE
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The full list of the 24 permutations is as follows (the present sequence tells where the 1's are):
1 2 3 4
2 1 4 3
2 4 1 3
4 2 3 1
4 3 2 1
3 4 1 2
3 1 4 2
1 3 2 4
1 3 4 2
3 1 2 4
3 2 1 4
2 3 4 1
2 4 3 1
4 2 1 3
4 1 2 3
1 4 3 2
1 4 2 3
4 1 3 2
4 3 1 2
3 4 2 1
3 2 4 1
2 3 1 4
2 1 3 4
1 2 4 3
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MAPLE
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ring:= proc(k) option remember; local l, a, b, c, swap, h; l:= [1, 2, 3, 4]; swap:= proc(i, j) h:=l[i]; l[i]:=l[j]; l[j]:=h end; a:= proc() swap(1, 2); swap(3, 4); l[k] end; b:= proc() swap(2, 3); l[k] end; c:= proc() swap(3, 4); l[k] end; [l[k], seq ([seq ([a(), b()][], j=1..3), a(), c()][], i=1..3)] end: bells:=[seq (ring(k), k=1..4)]: indx:= proc(l, n, k) local i; for i from 1 to 4 do if l[i][n]=k then break fi od; i end: a := n-> indx (bells, modp(n-1, 24)+1, 1): seq (a(n), n=1..99); [From Alois P. Heinz (heinz(AT)hs-heilbronn.de), Aug 19 2008]
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CROSSREFS
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Cf. A090277-A090284.
Sequence in context: A058339 A133852 A093150 this_sequence A051951 A107898 A128863
Adjacent sequences: A090278 A090279 A090280 this_sequence A090282 A090283 A090284
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KEYWORD
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nonn
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AUTHOR
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N. J. A. Sloane (njas(AT)research.att.com), Jan 24 2004
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