December 2006 - mathfun@mailman.xmission.com

[math-fun] Sudokus in other bases
by Mike Stay 11 Dec '06

11 Dec '06

http://xkcd.com/c74.html -- Mike Stay metaweta(a)gmail.com http://math.ucr.edu/~mike

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[math-fun] RE: Commas
by N. J. A. Sloane 11 Dec '06

11 Dec '06

Eric, please send that sequence in now, so that i can clean up my email stack! Best Neil

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[math-fun] News on Taxicab and Cabtaxi numbers
by Christian Boyer 11 Dec '06

11 Dec '06

The known information on Taxicab and Cabtaxi numbers goes up to Taxicab(6) and Cabtaxi(9). Here are new upper bounds, up to Taxicab(12) and Cabtaxi(20): http://cboyer.club.fr/Taxicab.htm A paper is in preparation. Christian.

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[math-fun] RE: Commas
by Eric Angelini 11 Dec '06

11 Dec '06

Hello Again Zak (and others) I've received this (coming from rec.puzzles) from "The Qurqirish Dragon": I noticed one problem with the rule. Take the sequence starting with 2: 2, (+22) 24, (+47) 71, ? Is the next value 89 or 90? Both follow the given rule: 2, (+22) 24, (+47) 71, (+18) 89, (+91) 180, ... 2, (+22) 24, (+47) 71, (+19) 90, (+09) 99, (+91) 190, ... This problem will happen whenever a given addition works resulting in a number consisting of all 9s (except for the first digit, which must be less than 9). What do you think about this remark? Can such a pb arise in the "main" sequence (the one starting with "1")? Do I have to rewrite the rule saying something like: "Keep the sequence as low as possible" Best, É.

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[math-fun] RE: Commas
by Eric Angelini 11 Dec '06

11 Dec '06

Thanks, Zak, beautiful! I had calculated by hand: 1,12,35,94,135,186,248,331,344,387,461,475,530,535,590,595,651, 667,744,791,809,908,997,1068,1149,1240,1241,1252,1273,1304,1345, 1396,1457,1528,1609,1700,1701,1712,1733,1764,1805,1856,1917,1988, 2070,2072,2094,2136,2198 ... which is exactly what you have got. I will submit this to Neil together with yr name in january. Best, É. (I'm interested in the first 1000 terms for my personal webpage, if you don't mind -- 1000 thanks again) -----Message d'origine----- De : zak seidov [mailto:zakseidov@yahoo.com] Envoyé : lundi 11 décembre 2006 17:46 À : Eric Angelini; math-fun; seqfan(a)ext.jussieu.fr Objet : Re: Commas Sequence is growing almost linearly (I calculated first 1000 terms), differences have some (nice) patterns. For checking purposes I give first and 10th hundreds terms of seq: {1,12,35,94,135,186,248,331,344,387,461,475,530,535,590,595,651,667,744,791,809,908,997,1068,1149,1240,1241,1252,1273,1304,1345,1396,1457,1528,1609,1700,1701,1712,1733,1764,1805,1856,1917,1988,2070,2072,2094,2136,2198,2280,2282,2304,2346,2408,2490,2492,2514,2556,2618,2700,2702,2724,2766,2828,2910,2912,2934,2976,3039,3132,3155,3208,3291,3304,3347,3420,3423,3456,3519,3612,3635,3688,3771,3784,3827,3900,3903,3936,3999,4093,4127,4201,4215,4269,4363,4397,4471,4485,4539,4633}<...>{44303,44337,44411,44425,44479,44573,44607,44681,44695,44749,44843,44877,44951,44965,45019,45113,45147,45221,45235,45289,45383,45417,45491,45505,45559,45653,45687,45761,45775,45829,45923,45957,46031,46045,46099,46193,46227,46301,46315,46369,46463,46497,46571,46585,46639,46733,46767,46841,46855,46909,47003,47037,47111,47125,47179,47273,47307,47381,47395,47449,47543,47577,47651,47665,47719,47813,47847,47921,47935,47989,48083,48117,48191,48205,48259,48353,48387,48461,48475,48529,48623,48657,48731,48745,48799 ,48893,48927,49001,49015,49069,49163,49197,49271,49285,49339,49433,49467,49541,49555,49609} Zak For those interesting I can send also graphs. --- Eric Angelini <Eric.Angelini(a)kntv.be> wrote: > > For non-mathematicians only: > http://www.cetteadressecomportecinquantesignes.com/Commas.htm > Best, > É. > > __________________________________________________ Do You Yahoo!? Tired of spam? Yahoo! Mail has the best spam protection around http://mail.yahoo.com

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[math-fun] Commas
by Eric Angelini 11 Dec '06

11 Dec '06

For non-mathematicians only: http://www.cetteadressecomportecinquantesignes.com/Commas.htm Best, É.

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Re: Re: [math-fun] Add no digit of n to n
by Michael Kleber 11 Dec '06

11 Dec '06

Paul R. Pudaite <pudaite(a)pipeline.com> wrote: > For binary numbers, the sequence has one term (no iterations): 1. :) Hmm, good point: 2 1 3 12 4 132 5 1324 6 12543 7 123546 8 1234576 9 12345876 10 123456978, as before; this is the first one that takes significant time to compute. f[x_,b_] := x + Module[{y=Complement[Range[b-1],IntegerDigits[x,b]]},If[Length[y]>0,Min[y],0]] g[b_] := Print @@ IntegerDigits[FixedPoint[f[#,b]&,1], b] --Michael Kleber -- It is very dark and after 2000. If you continue you are likely to be eaten by a bleen.

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[math-fun] Add no digit of n to n
by Eric Angelini 11 Dec '06

11 Dec '06

Hello Math-Fun, What is the last term of the sequence starting with "1" and obeying the rule: "Add to n the smallest positive integer sharing no digit with n" Sequence should begin like this : 1,3,4,5,6,7,8,9,10,12,15,17,19,21,24,25.... Best, E.

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RE : [math-fun] Add no digit of n to n
by Eric Angelini 10 Dec '06

10 Dec '06

Michael, you are the best! You'll enter soon my webpage about this seq. -- what about that! ;-) Thanks, E. ________________________________ De: math-fun-bounces+eric.angelini=kntv.be(a)mailman.xmission.com de la part de Michael Kleber Date: dim. 10/12/2006 20:45 À: math-fun Objet : Re: [math-fun] Add no digit of n to n 123456978, after 65627501 iterations. What did we do before computers could do millions of pointless calculations for us?... --Michael On 12/10/06, Eric Angelini <Eric.Angelini(a)kntv.be> wrote: > > > Hello Math-Fun, > > What is the last term of the sequence starting with "1" and obeying the rule: > > "Add to n the smallest positive integer sharing no digit with n" > > Sequence should begin like this : > > 1,3,4,5,6,7,8,9,10,12,15,17,19,21,24,25.... > > Best, > > E. > > _______________________________________________ > math-fun mailing list > math-fun(a)mailman.xmission.com > http://mailman.xmission.com/cgi-bin/mailman/listinfo/math-fun > -- It is very dark and after 2000. If you continue you are likely to be eaten by a bleen. _______________________________________________ math-fun mailing list math-fun(a)mailman.xmission.com http://mailman.xmission.com/cgi-bin/mailman/listinfo/math-fun

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[math-fun] Is this familiar? For any f,
by R. William Gosper 10 Dec '06

10 Dec '06

j j ==== /===\ \ 2 j n | | n n 2 j > ( ) (- 1) | | (f(k) - -) (1 + -) = ( ). / j - n | | k k j ==== k = 1 n = 0 E.g., for f:=1-ap^(k-1) j j ==== /===\ \ 2 j n | | n n k-1 > ( ) (- 1) | | (1 + -) (1 - - - a p ) / j - n | | k k ==== k = 1 n = 1 (a; p) = 1 - ----------------------------------------------------- . j 2 j ( ) j --rwg

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