Search: id:A075226
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%I A075226
%S A075226 3,11,19,137,137,1019,2143,7129,7129,78167,81401,1085933,1111673,
%T A075226 1165727,2364487,41325407,41325407,796326437,809074601,812400209,
%U A075226 822981689,19174119571,19652175721,99554817251,100483070801
%N A075226 Largest prime in the numerator of the 2^n sums generated from the set 
               1, 1/2, 1/3,..., 1/n.
%C A075226 For the smallest odd prime not generated, see A075227. For information 
               about how often the numerator of these sums is prime, see A075188 
               and A075189. The Mathematica program also prints the subset that 
               yields the largest prime. For n <=20, the largest prime occurs in 
               a sum of n-2, n-1, or n reciprocals.
%H A075226 Martin Fuller, <a href="b075226.txt">Table of n, a(n) for n = 2..100</
               a>
%H A075226 Martin Fuller, <a href="a075226.gp.txt">PARI program</a>
%e A075226 a(3) =11 because 11 is largest prime numerator in the three sums that 
               yield primes: 1+1/2 = 3/2, 1/2+1/3 = 5/6 and 1+1/2+1/3 = 11/6.
%t A075226 Needs["DiscreteMath`Combinatorica`"]; maxN=20; For[t={}; lst={}; mx=0; 
               i=0; n=2, n<=maxN, n++, While[i<2^n-1, i++; s=NthSubset[i, Range[n]]; 
               k=Numerator[Plus@@(1/s)]; If[PrimeQ[k], If[k>mx, t=s]; mx=Max[mx, 
               k]]]; Print[n, " ", t]; AppendTo[lst, mx]]; lst
%Y A075226 Cf. A001008, A075135, A075188, A075189, A075227.
%Y A075226 Sequence in context: A048270 A088733 A128996 this_sequence A028978 A082628 
               A166096
%Y A075226 Adjacent sequences: A075223 A075224 A075225 this_sequence A075227 A075228 
               A075229
%K A075226 nice,nonn
%O A075226 2,1
%A A075226 T. D. Noe (noe(AT)sspectra.com), Sep 08 2002
%E A075226 More terms from Martin Fuller (martin_n_fuller(AT)btinternet.com), Jan 
               19 2008

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