

A083776


The nth row of the following triangle contains n distinct primes such that the product of (n1) of them + 2 is prime in all cases. The first (n1) numbers are the smallest set whose product +2 is a prime and the nth term is chosen to satisfy the requirement. a(1) = 2 by convention. Sequence contains the triangle by rows.


2



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, 12653, 3, 5, 7, 11, 13, 17, 31, 92467, 3, 5, 7, 11, 13, 17, 19, 37, 342362509
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OFFSET

1,1


COMMENTS

Perhaps the sequence is finite in the sense there exists some n for which the nth term ( the last term ) of the row does not exist.


LINKS



EXAMPLE

2
3 5
3 5 7
3 5 7 31
...


PROG

(PARI) row(n) = {if(n==1, return([2])); my(c=1, p=prime(n), v=vector(n2, i, prime(i+1)), w); while(!isprime(vecprod(v)*p+2), p=nextprime(p+1)); v=concat(v, p); w=vector(n1, 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


CROSSREFS



KEYWORD



AUTHOR

Amarnath Murthy and Meenakshi Srikanth (menakan_s(AT)yahoo.com), May 07 2003


EXTENSIONS



STATUS

approved



