A083773 The n-th row of the following triangle contains n distinct numbers such that the product of (n-1) of them + 1 is always a prime. The first (n-1) numbers are the smallest set whose product +1 is a prime and the n-th term is chosen to satisfy the requirement. a(1) = 1 by convention. Sequence contains the triangle by rows.

1, 1, 2, 1, 2, 6, 1, 2, 3, 6, 1, 2, 3, 5, 18, 1, 2, 3, 4, 8, 2275, 1, 2, 3, 4, 5, 10, 222, 1, 2, 3, 4, 5, 6, 9, 762986, 1, 2, 3, 4, 5, 6, 7, 9, 2203418, 1, 2, 3, 4, 5, 6, 7, 8, 15

Offset

1,3

Links

Table of n, a(n) for n=1..54.

Example

1
1 2
1 2 6
1 2 3 6
1 2 3 5 18
...

Prog

(PARI) fac = 1; for (n = 1, 40, fac *= n; for (i = 1, n, print1(i); print1(" ")); i = n + 1; while (!isprime(fac*i + 1), i++); print1(i); print1(" "); fails = 1; j = i; while (fails, j++; fails = !isprime(j*fac + 1); k = 1; while (!fails && k <= n, if (isprime(j*i*fac/k + 1), k++, fails = 1))); print(j));

Crossrefs

Cf. A083774, A083775.

Sequence in context: A159885 A178803 A292901 * A129116 A096179 A361834

Adjacent sequences: A083770 A083771 A083772 * A083774 A083775 A083776

Keyword

more,nonn,tabl

Author

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

Extensions

More terms from David Wasserman, Nov 29 2004

Status

approved