%N A variation of the 'viral sequence' A334355; the same rules for a(n) apply but all numbers must be prime.
%C See A334355 for a description of the rules determining a(n). This sequence follows the same rules except that all terms must be prime.
%C Note that as the sequence starts with 2,7,3,... where 2+7+1=10 is a nonprime and 7+3+1=11 is a prime, like A334355 the terms in this sequence are therefore locked into a pattern of alternating pairs which when 1 is added form a nonprime and then a prime.
%H Scott R. Shannon, <a href="/A330883/b330883.txt">Table of n, a(n) for n = 1..10000</a>
%e a(1) = 2, the smallest prime.
%e a(2) = 7 as a(1)+a(2) = 2+7 = 9 is a composite. Note that a(2) could not be 4 or 6 as only prime numbers are allowed, nor could it be 3 or 5 as 2+3=5 is a prime and 2+5=7 is a prime.
%e a(3) = 3 as a(2)+a(3) = 7+3 = 10 is a composite, and 3 is the smallest prime not yet appearing that sums with 7 to form a composite.
%Y Cf. A334355, A000040, A002808, A001043.
%A _Scott R. Shannon_ and _Eric Angelini_, Apr 30 2020