1. A clothing catalog that came the other day was selling T-shirts saying Here's looking at [drawing of man with beard] Euclid 2. I sent the following to the seqfan mailing list, but got no takers. Dear Seqfans, I added 8 sequences from "Plain Bob Minimus" in bell-ringing, see below. This is a change-ringing method for 4 bells. (This was prompted by the cover of the Jan 2004 Notices AMS.) I would like to get further sequences of this type, if someone would be willing to work them out. There are many possibilities: Treble Bob, Stedman Triples, ... The links below give further information. With n bells, the sequences have period n!, so 5-bell sequences would just fit; for 6 or more bells it will only be possible to give the beginning of the sequences. It would be nice if someone would pick up the bell here and run with it. NJAS %I A090277 %S A090277 1,2,2,4,4,3,3,1,1,3,3,2,2,4,4,1,1,4,4,3,3,2,2,1,1,2,2,4,4,3,3,1,1, %T A090277 3,3,2,2,4,4,1,1,4,4,3,3,2,2,1,1,2,2,4,4,3,3,1,1,3,3,2,2,4,4,1,1,4, %U A090277 4,3,3,2,2,1,1,2,2,4,4,3,3,1,1,3,3,2,2,4,4,1,1,4,4,3,3,2,2,1,1,2,2 %N A090277 "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 number in position 1 of n-th permutation. %H A090277 Rober Bailey, <a href="http://www.ringing.info">Change Ringing Resources</a> %H A090277 David Joyner, <a href="http://web.usna.navy.mil/~wdj/book/node158.html">Application: Bell Ringing</a> %H A090277 M.I.T. Bell-Ringers, <a href="http://web.mit.edu/bellringers/www/html/change_instruction.html">General Information On Change Ringing</a> %F A090277 Period 24. %e A090277 The full list of the 24 permutations is as follows (the present sequence gives the first column): %e A090277 1 2 3 4 %e A090277 2 1 4 3 %e A090277 2 4 1 3 %e A090277 4 2 3 1 %e A090277 4 3 2 1 %e A090277 3 4 1 2 %e A090277 3 1 4 2 %e A090277 1 3 2 4 %e A090277 1 3 4 2 %e A090277 3 1 2 4 %e A090277 3 2 1 4 %e A090277 2 3 4 1 %e A090277 2 4 3 1 %e A090277 4 2 1 3 %e A090277 4 1 2 3 %e A090277 1 4 3 2 %e A090277 1 4 2 3 %e A090277 4 1 3 2 %e A090277 4 3 1 2 %e A090277 3 4 2 1 %e A090277 3 2 4 1 %e A090277 2 3 1 4 %e A090277 2 1 3 4 %e A090277 1 2 4 3 %Y A090277 Cf. A090278-A090284. %K A090277 nonn,new %O A090277 1,2 %A A090277 njas, Jan 24 2004 %I A090278 %S A090278 2,1,4,2,3,4,1,3,3,1,2,3,4,2,1,4,4,1,3,4,2,3,1,2,2,1,4,2,3,4,1,3,3, %T A090278 1,2,3,4,2,1,4,4,1,3,4,2,3,1,2,2,1,4,2,3,4,1,3,3,1,2,3,4,2,1,4,4,1, %U A090278 3,4,2,3,1,2,2,1,4,2,3,4,1,3,3,1,2,3,4,2,1,4,4,1,3,4,2,3,1,2,2,1,4 %N A090278 "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 number in position 2 of n-th permutation. %H A090278 Rober Bailey, <a href="http://www.ringing.info">Change Ringing Resources</a> %H A090278 David Joyner, <a href="http://web.usna.navy.mil/~wdj/book/node158.html">Application: Bell Ringing</a> %F A090278 Period 24. %Y A090278 Cf. A090277-A090284. %K A090278 nonn,new %O A090278 1,1 %A A090278 njas, Jan 24 2004 %I A090279 %S A090279 3,4,1,3,2,1,4,2,4,2,1,4,3,1,2,3,2,3,1,2,4,1,3,4,3,4,1,3,2,1,4,2,4, %T A090279 2,1,4,3,1,2,3,2,3,1,2,4,1,3,4,3,4,1,3,2,1,4,2,4,2,1,4,3,1,2,3,2,3, %U A090279 1,2,4,1,3,4,3,4,1,3,2,1,4,2,4,2,1,4,3,1,2,3,2,3,1,2,4,1,3,4,3,4,1 %N A090279 "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 number in position 3 of n-th permutation. %H A090279 Rober Bailey, <a href="http://www.ringing.info">Change Ringing Resources</a> %H A090279 David Joyner, <a href="http://web.usna.navy.mil/~wdj/book/node158.html">Application: Bell Ringing</a> %F A090279 Period 24. %Y A090279 Cf. A090277-A090284. %K A090279 nonn,new %O A090279 1,1 %A A090279 njas, Jan 24 2004 %I A090280 %S A090280 4,3,3,1,1,2,2,4,2,4,4,1,1,3,3,2,3,2,2,1,1,4,4,3,4,3,3,1,1,2,2,4,2, %T A090280 4,4,1,1,3,3,2,3,2,2,1,1,4,4,3,4,3,3,1,1,2,2,4,2,4,4,1,1,3,3,2,3,2, %U A090280 2,1,1,4,4,3,4,3,3,1,1,2,2,4,2,4,4,1,1,3,3,2,3,2,2,1,1,4,4,3,4,3,3 %N A090280 "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 number in position 4 of n-th permutation. %H A090280 Rober Bailey, <a href="http://www.ringing.info">Change Ringing Resources</a> %H A090280 David Joyner, <a href="http://web.usna.navy.mil/~wdj/book/node158.html">Application: Bell Ringing</a> %F A090280 Period 24. %Y A090280 Cf. A090277-A090284. %K A090280 nonn,new %O A090280 1,1 %A A090280 njas, Jan 24 2004 %I A090281 %S A090281 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, %T A090281 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, %U A090281 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 %N A090281 "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. %C A090281 This is the "plain hunting" sequence with 4 bells. %H A090281 Rober Bailey, <a href="http://www.ringing.info">Change Ringing Resources</a> %H A090281 David Joyner, <a href="http://web.usna.navy.mil/~wdj/book/node158.html"> Application: Bell Ringing</a> %H A090281 M.I.T. Bell-Ringers, <a href="http://web.mit.edu/bellringers/www/html/change_instruction.html">General Information On Change Ringing</a> %F A090281 Period 24. %e A090281 The full list of the 24 permutations is as follows (the present sequence tells where the 1's are): %e A090281 1 2 3 4 %e A090281 2 1 4 3 %e A090281 2 4 1 3 %e A090281 4 2 3 1 %e A090281 4 3 2 1 %e A090281 3 4 1 2 %e A090281 3 1 4 2 %e A090281 1 3 2 4 %e A090281 1 3 4 2 %e A090281 3 1 2 4 %e A090281 3 2 1 4 %e A090281 2 3 4 1 %e A090281 2 4 3 1 %e A090281 4 2 1 3 %e A090281 4 1 2 3 %e A090281 1 4 3 2 %e A090281 1 4 2 3 %e A090281 4 1 3 2 %e A090281 4 3 1 2 %e A090281 3 4 2 1 %e A090281 3 2 4 1 %e A090281 2 3 1 4 %e A090281 2 1 3 4 %e A090281 1 2 4 3 %Y A090281 Cf. A090277-A090284. %K A090281 nonn,new %O A090281 1,2 %A A090281 njas, Jan 24 2004 %I A090282 %S A090282 2,1,1,2,3,4,4,3,4,3,2,1,1,2,3,4,3,4,4,3,2,1,1,2,2,1,1,2,3,4,4,3,4, %T A090282 3,2,1,1,2,3,4,3,4,4,3,2,1,1,2,2,1,1,2,3,4,4,3,4,3,2,1,1,2,3,4,3,4, %U A090282 4,3,2,1,1,2,2,1,1,2,3,4,4,3,4,3,2,1,1,2,3,4,3,4,4,3,2,1,1,2,2,1,1 %N A090282 "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 2 in n-th permutation. %H A090282 David Joyner, <a href="http://web.usna.navy.mil/~wdj/book/node158.html"> Application: Bell Ringing</a> %F A090282 Period 24. %Y A090282 Cf. A090277-A090284. %K A090282 nonn,new %O A090282 1,1 %A A090282 njas, Jan 24 2004 %I A090283 %S A090283 3,4,4,3,2,1,1,2,2,1,1,2,3,4,4,3,4,3,2,1,1,2,3,4,3,4,4,3,2,1,1,2,2, %T A090283 1,1,2,3,4,4,3,4,3,2,1,1,2,3,4,3,4,4,3,2,1,1,2,2,1,1,2,3,4,4,3,4,3, %U A090283 2,1,1,2,3,4,3,4,4,3,2,1,1,2,2,1,1,2,3,4,4,3,4,3,2,1,1,2,3,4,3,4,4 %N A090283 "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 3 in n-th permutation. %H A090283 David Joyner, <a href="http://web.usna.navy.mil/~wdj/book/node158.html"> Application: Bell Ringing</a> %F A090283 Period 24. %Y A090283 Cf. A090277-A090284. %K A090283 nonn,new %O A090283 1,1 %A A090283 njas, Jan 24 2004 %I A090284 %S A090284 4,3,2,1,1,2,3,4,3,4,4,3,2,1,1,2,2,1,1,2,3,4,4,3,4,3,2,1,1,2,3,4,3, %T A090284 4,4,3,2,1,1,2,2,1,1,2,3,4,4,3,4,3,2,1,1,2,3,4,3,4,4,3,2,1,1,2,2,1, %U A090284 1,2,3,4,4,3,4,3,2,1,1,2,3,4,3,4,4,3,2,1,1,2,2,1,1,2,3,4,4,3,4,3,2 %N A090284 "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 4 (the tenor bell) in n-th permutation. %H A090284 David Joyner, <a href="http://web.usna.navy.mil/~wdj/book/node158.html"> Application: Bell Ringing</a> %F A090284 Period 24. %Y A090284 Cf. A090277-A090283. %K A090284 nonn,new %O A090284 1,1 %A A090284 njas, Jan 24 2004