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The classic string "Hello world!" can be translated to list of characters with ascii-codes:

[72; 101; 108; 108; 111; 32; 87; 111; 114; 108; 100; 33] 

Is there a mathematical function to generate this sequence of numbers (without explicitly enumerating them)?

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    @J.M.: I consider mathematics as the base language, from which everything else is derived. As such it is capable of simplification and adding complexity, it need not be restricted.2011-04-30

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Yes, see below but you probably do not want this. It is certainly less compact than the original list of values because you have to store more than twice the amount of data, if you want exact rational coefficients. Moreover, if you're writing a program, beware that 19531322383 does not fit in 32 bits.

enter image description here

http://www.wolframalpha.com/input/?i=interpolate+72+101+108+108+111+32+87+111+114+108+100+33

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    @Willi: sure - I only just couldn't resist... ;-) (Question is closed anyway)2011-04-29
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A -likely- nonexpected answer provides the following link. However, the resulting formula is much more messy than the interpolation-formula...
See http://www.xamuel.com/inverse-graphing-calculator.php?phrase=Hello+World and have fun...

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    That's fun but it generates an *image*, not values.2011-04-29