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%I #5 Mar 30 2012 17:27:39
%S 5,7,11,5,7,11,13,17,23,23,31,31,37,41,47,53,53,61,61,67,73,73,83,89,
%T 89,97,101,103,107,113,113,131,131,139,139,151,157,157,167,173,173,
%U 181,181,191,193,199,211,211,223,227,233,233,241,251,257,263,263,271,271,277
%N Let P = { p_1 = 3, p_2 = 5, ...} be the set of odd primes. If p_n in P can be written as p_n = q+r+s with q, r, s in P, let a(n) = largest such q, otherwise let a(n) = p_{n+1}.
%C 11 belongs to a cycle of length 3 when a(n) is iterated. The paper by Janos studies the set of cycles.
%D Ludvik Janos, On Vinagradov's 3-primes theorem, Abstracts Amer. Math. Soc., 25 (No. 2, 2002), p. 398, #01T-11-57.
%e 3 has no such representation, so a(1) = 5. The 10th odd prime, 31, equals 23+5+3, with q=23 and no larger q exists, so a(1) = 23.
%o (PARI) {forprime(p=3,300,b=0; q=precprime(p-1); while(b<1&&q>2,r=q; while(b<1&&r>2,s=r; while(b<1&&s>2,if(q+r+s==p,b=1; print1(q,","),s=precprime(s-1))); r=precprime(r-1)); q=precprime(q-1)); if(b<1,print1(nextprime(p+1),",")))}
%K nonn,easy
%O 1,1
%A _N. J. A. Sloane_, Apr 25 2003
%E Are there other cycles? - _N. J. A. Sloane_.
%E More terms and PARI code from _Klaus Brockhaus_, Apr 26 2003
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