A083776 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.

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

Offset

1,1

Comments

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.

Links

Table of n, a(n) for n=1..45.

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(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

Crossrefs

Cf. A083777, A083778, A083773.

Sequence in context: A077276 A073684 A179295 * A122820 A261324 A224887

Adjacent sequences: A083773 A083774 A083775 * A083777 A083778 A083779

Keyword

nonn,tabl,more

Author

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

Extensions

More terms from David Wasserman, Nov 29 2004

Corrected by Ray Chandler, Oct 04 2006

a(45) from Jinyuan Wang, May 23 2020

Status

approved