Besides Mike and Andy, a third kind soul also pointed out to me the triviality of my question. It goes without saying that . (I had just run into the question of what is the largest number that is not a natural combination of two relatively prime natural numbers A and B, and the rest is history stupid.) ——Dan P.S. Hmm, I guess it might be interesting to ask the same question after replacing P_n := {p_1,...,p_n} by the infinite set of all primes but the first n of them: Q_n := {p_(n+1),...,p_(n+k),...}. P.P.S. My mathematical thinking has been heedless, headlong, and willy-nilly at least since 6th grade, when after my pleading, my elementary school teacher promised to teach me algebra if I got 3 consecutive perfect scores on our weekly arithmetic tests. I never managed to do so, solely because of careless error.
On May 15, 2015, at 7:09 AM, Mike Speciner <ms@alum.mit.edu> wrote:
f(1) ?
If p_1 = 2, then f(2+) = 1 [2(k+1)+3*0, 2k+3*1]
If p_1 = 3, then f(2) = 7, [3(k+3)+5*0, 3(k+1)+5*1, 3k+5*2] f(3+) = 4, [above, 7*1, 3*2, 5*1]
Am I confused, or did I completely misunderstand what you've written?
--ms
On 14-May-15 23:57, Dan Asimov wrote:
I recently read that every sufficiently large integer in Z+ is representable as a linear combination — with coefficients in N_0 := {0,1,2,...} — of the first n primes
P_n := {p_1,...,p_n} .
(Actually this holds for relatively prime integers.)
Let f(n) denote the largest integer *not* expressible as an N_0 combination of the primes in P_n with all coefficients nonnegative.
I've also read there is no known expression for f(n).
So: Is there a simple asymptotic expression for f(n) as n -> oo ???
——Dan _______________________________________________ math-fun mailing list math-fun@mailman.xmission.com https://mailman.xmission.com/cgi-bin/mailman/listinfo/math-fun
_______________________________________________ math-fun mailing list math-fun@mailman.xmission.com https://mailman.xmission.com/cgi-bin/mailman/listinfo/math-fun