One word, Mike : perfect ! Best, É. (my longest ending tail -- starting the loop with 5 : 5 3 2 11 6 5 14 9 5 4 13 8 5 3 2 11 6 5 14 9 5 4 13 7 6 15 8 7 16 9 7 25 END ) ^^^^^^ ^^^^^^ -----Message d'origine----- De : math-fun-bounces+eric.angelini=kntv.be@mailman.xmission.com [mailto:math-fun-bounces+eric.angelini=kntv.be@mailman.xmission.com] De la part de Mike Stay Envoyé : mardi 6 décembre 2005 18:01 À : math-fun Objet : Re: [math-fun] 2-digits sum loop

Hello, consider this « sequence » :

17, 9, 8, 17, 9, 8, 17, 9, 8, 17, 9, 8, ...

... it's property is that any n is the sum of the two digits immediately following n.

... the seq. is built on the repeated pattern : [17, 9, 8]

Find another such seq. built on a different pattern.

There's the nice sequence 0,0,0,... ;) Sequences should really be built in reverse, since then the next term is forced. It's convenient to start with the cycle forced by 11: 11,6,5,14,9,5,4,13,8,5,3,2,11 This cycle is also the one forced by 13 and 14. 12 falls into the same cycle immediately: ...,5,3,12 15 and 16 take a little longer: ...,13,7,6,15,8,7,16 17 is the cycle you noted: 17,9,8,17 18 falls into the 11-cycle ...2,1,10,9,18 Whatever number you start with, the sum of the first two digits will be a number less than 19. I think the longest finite tail before reaching a two digit number is starting with 1,0, which gives the 11-cycle.

Best, É.

-- Mike Stay metaweta@gmail.com http://math.ucr.edu/~mike _______________________________________________ math-fun mailing list math-fun@mailman.xmission.com http://mailman.xmission.com/cgi-bin/mailman/listinfo/math-fun