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%I #17 May 24 2020 01:46:32
%S 2,3,5,3,5,7,3,5,7,31,3,5,7,13,127,3,5,7,11,13,149,3,5,7,11,13,19,
%T 12653,3,5,7,11,13,17,31,92467,3,5,7,11,13,17,19,37,342362509
%N The n-th row of the following triangle contains n distinct primes such that the product of (n-1) of them + 2 is prime in all cases. The first (n-1) numbers are the smallest set whose product +2 is a prime and the n-th term is chosen to satisfy the requirement. a(1) = 2 by convention. Sequence contains the triangle by rows.
%C Perhaps the sequence is finite in the sense there exists some n for which the n-th term ( the last term ) of the row does not exist.
%e 2
%e 3 5
%e 3 5 7
%e 3 5 7 31
%e ...
%o (PARI) row(n) = {if(n==1, return([2])); my(c=1, p=prime(n), v=vector(n-2, i, prime(i+1)), w); while(!isprime(vecprod(v)*p+2), p=nextprime(p+1)); v=concat(v, p); w=vector(n-1, i, vecprod(v)/v[i]); while(c<n, c=1; p=nextprime(p+1); while(c<n && isprime(w[c]*p+2), c++)); concat(v, p); } \\ _Jinyuan Wang_, May 23 2020
%Y Cf. A083777, A083778, A083773.
%K nonn,tabl,more
%O 1,1
%A _Amarnath Murthy_ and Meenakshi Srikanth (menakan_s(AT)yahoo.com), May 07 2003
%E More terms from _David Wasserman_, Nov 29 2004
%E Corrected by _Ray Chandler_, Oct 04 2006
%E a(45) from _Jinyuan Wang_, May 23 2020
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