it would be more in the spirit to have an infinitely long sequence which contained an infinite number of different positive integers. i believe it is possible for E, though i can't prove it. i suspect it may also be possible for other letters like T. erich On Dec 15, 2011, at 8:56 AM, Eric Angelini wrote:
One FOUR too much in the last morphism line, sorry. Should read:
... Here we go to infinity thanks to the morphism:
FOUR --> NINE NINE --> FORTY-FIVE FORTY-FIVE --> FOUR FOUR FOUR FOUR FOUR FOUR FOUR FOUR FOUR FORTY-FIVE
E = SIX TWENTY FOUR FOUR FORTY-FIVE NINE NINE FOUR FOUR FOUR FOUR FOUR FOUR FOUR FOUR FOUR FORTY-FIVE FORTY-FIVE FORTY-FIVE NINE NINE NINE NINE NINE NINE NINE NINE NINE FOUR FOUR FOUR FOUR FOUR FOUR FOUR FOUR FOUR FORTY-FIVE ...
Best, É.
-----Message d'origine----- De : Eric Angelini Envoyé : jeudi 15 décembre 2011 14:53 À : 'math-fun' Objet : RE: [math-fun] A Xmas present
Erich Friedman: this is about as long as i could get with a reasonable ending:
six, one, eight, five, two, seven, six, one, fourteen, two, four, four, seven, one, nine, two, three, two, four, seven, seven, one, four, one, two, three, three, sequence.
Eric A.: draw a thin vertical stroke after each letter "e". Count the letters between the strokes. Enjoy!
... Here we go to infinity thanks to the morphism:
FOUR --> NINE NINE --> FORTY-FIVE FORTY-FIVE --> FOUR FOUR FOUR FOUR FOUR FOUR FOUR FOUR FOUR FOUR FORTY-FIVE
E = SIX TWENTY FOUR FOUR FORTY-FIVE NINE NINE FOUR FOUR FOUR FOUR FOUR FOUR FOUR FOUR FOUR FOUR FORTY-FIVE FORTY-FIVE FORTY-FIVE NINE NINE NINE NINE NINE NINE NINE NINE NINE FOUR FOUR FOUR FOUR FOUR FOUR FOUR FOUR FOUR FORTY-FIVE ...
Best, É.
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