A330612 Plain Bob Infinity. Select terms <= n to get a permutation whose powers generate all possible pairs of bells for change ringing.

2, 3, 5, 1, 7, 4, 9, 6, 11, 8, 13, 10, 15, 12, 17, 14, 19, 16, 21, 18, 23, 20, 25, 22, 27, 24, 29, 26, 31, 28, 33, 30, 35, 32, 37, 34, 39, 36, 41, 38, 43, 40, 45, 42, 47, 44, 49, 46, 51, 48, 53, 50, 55, 52, 57, 54, 59, 56, 61, 58, 63, 60, 65, 62, 67, 64, 69, 66, 71, 68, 73, 70, 75, 72, 77, 74, 79, 76, 81, 78, 80

Offset

1,1

Comments

Powers of permutation 235174968, taken in the initial four pairs of 2, generate all 36 pairs of 9 bells, making this a Plain Bob Caters rule. Words for three to twelve bells are Singles, Minimus, Doubles, Minor, Triples, Major, Caters, Royal, Cinques and Maximus.

2 3 5 1 7 4 9 6 8 10 -- The terms <= 10 give a Plain Bob Royal generator.

2 3 5 1 7 4 6 8 -- The terms <= 8 give a Plain Bob Major generator: 23 51 74 68, 35 72 61 48, 57 63 42 18, 76 45 13 28, 64 17 25 38, 41 26 37 58, 12 34 56 78.

Links

Table of n, a(n) for n=1..81.

Richard Duckworth and Fabian Stedman, Tintinnalogia, or, the Art of Ringing, (1671). Released by Project Gutenberg, 2006.

Wikipedia, Method ringing

Mathematica

Nest[Insert[Append[#, Max[#] + 1], Max[#] + 2, -3] &, {2, 3, 1}, 39]

Crossrefs

Sequence in context: A210945 A372112 A191795 * A121053 A203620 A249070

Adjacent sequences: A330609 A330610 A330611 * A330613 A330614 A330615

Keyword

nonn,easy

Author

Ed Pegg Jr, Dec 20 2019

Status

approved