Talk:Friedman number

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The most reliable source I can find for the name Friedman number is Sloane's OEIS, A036057 and A080035. PrimeFan 16:59, 25 Aug 2004 (UTC)

Is there a better word than "lame"? Perhaps "trivial" would be more appropriate, or at least sound more like an encyclopedic/mathematical term. Confusing Manifestation 15:55, 30 January 2006 (UTC)

maybe, but I don't think its "trivial." That 12 is a divisor of 12, that's trivial, though valid. That 12 is a Friedman number cause 12 = (12) that's invalid, not trivial. Numerao 22:28, 30 January 2006 (UTC)

But if you did allow those sorts of things, then it would become trivial because then all integers would be Friedman numbers. So in other words, the rules for forming a Friedman number are defined to avoid trivial solutions. (Similar to how Fermat's Last Theorem is defined to avoid the trivial cases of n=2 or (x,y,z)=(1,0,1).) Confusing Manifestation 15:43, 31 January 2006 (UTC)

While there's a certain informal charm to using the word "lame," this might be one case where the word "trivial" makes more sense. I've changed the article thus. Anton Mravcek 21:26, 31 January 2006 (UTC)

[edit] On the smallest repdigits

Hi, am I missing something here, or is it simply straightforward to go ahead and check this claim about the smallest repdigits number which is also a Friedman number? It seems to me that there is an algorithm which will determine whether or not a number is Friedman in finite time, as there are only finitely many ways to combine things, and then just run it on the repdigit numbers. --Deville (Talk) 01:01, 30 March 2006 (UTC)

I don't think you're missing anything. There is an algorithm that will check whether an integer is a Friedman number in finite time, and efficiently too, but to my knowledge, Friedman's students haven't published it.

The only other algorithm I can think of is the one mentioned in the article, of checking a number against each possible expression. To implement that algorithm, it would first be necessary to catalog all possible Friedman expressions up to 8 digits.

It would still run in finite time, but wouldn't be for the impatient, even if we limit it to the repdigits. PrimeFan 16:11, 30 March 2006 (UTC)