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%I #14 Mar 04 2015 20:47:43
%S 3,5,11,7,13,17,23,19,29,31,37,41,53,43,61,47,59,67,71,73,79,89,83,97,
%T 101,109,103,137,107,139,113,127,149,157,151,131,167,163,173,211,179,
%U 181,197,191,199,223,239,229,193,251,233,277,241,269,263,307,227,293
%N a(1)=3, a(2)=5; for n > 2, a(n) = smallest prime not included earlier such that a(n-2) + a(n-1) + a(n) is a prime.
%C Primes which are less than some previous term: 7, 19, 43, 47, 83, 103, 107, 113, ...
%C In the first 10000 terms the range of the differences between primepi(a(i)) and (i+1) is from -39 to 78.
%C In the first 10000 terms the range of the differences between a(i) and the (i+1)th prime is from -416 to 912.
%C Conjecture: Every odd prime eventually appears; a(n) ~ prime(n).
%H Robert G. Wilson v, <a href="/A073653/b073653.txt">Table of n, a(n) for n = 1..10000</a>
%e a(3)=11 because 3 + 5 + 7 = 15 is composite and 3 + 5 + 11 = 19 is prime.
%t f[s_List] := Block[{p = s[[-2]] + s[[-1]], q = 7}, While[ !PrimeQ[p + q] || MemberQ[s, q], q = NextPrime[q]]; Append[s, q]]; Nest[f, {3, 5}, 56] (* _Robert G. Wilson v_, Mar 19 2012 *)
%Y Cf. A073654.
%K nonn
%O 1,1
%A _Amarnath Murthy_, Aug 10 2002
%E More terms from _Sascha Kurz_, Jan 28 2003
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