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%I #13 May 24 2013 13:07:17
%S 5,7,11,23,41,71,101,179,257,443,521,971,1499,2477,2927,3191,3719,
%T 6917,9851,13577,16061,25919,39503,53087,56813,96323,149417,245747,
%U 342077,491501,494699,986207,1231961,1726667,2068751,2165081,4233839,5220053,5714759,7879847
%N a(n) is the largest prime that is a sum of some 3 distinct previous terms.
%C Initial terms {2,3,5} and {3,5,7} give no prime, hence we start with a(1..3) = {5, 7, 11}.
%C Is the sequence infinite?
%C The Mathematica program is fast because it uses that fact that 7 must be one of the three numbers in the sum. Note that p = 5 (mod 6) for all terms but 7. - _T. D. Noe_, May 24 2013
%H Zak Seidov and T. D. Noe, <a href="/A226027/b226027.txt">Table of n, a(n) for n = 1..500</a> (first 123 from Zak Seidov)
%t t = {5, 11}; Do[u = Subsets[t, {2}]; w = Reverse[Sort[7 + Total /@ u]]; s = Select[w, PrimeQ, 1]; mx = s[[1]]; AppendTo[t, mx], {97}]; t = Insert[t, 7, 2] (* _T. D. Noe_, May 24 2013 *)
%o (PARI) N=50; v=vector(N); v[1]=5; v[2]=7; v[3]=11; n=3; while(n<N, m=0; for(i=1, n, for(j=i+1, n, for(k=j+1, n, t=v[i]+v[j]+v[k]; if(t>m && isprime(t), m=t)))); if(m>0, n++; v[n]=m)); v /* from _Ralf Stephan_ */
%K nonn
%O 1,1
%A _Zak Seidov_, May 23 2013
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