A178916 Triangular array a(n,k) read by rows: nextprime(k*n!)-k*n!. For 1<=k<=n.

1, 1, 1, 1, 1, 1, 5, 5, 1, 1, 7, 1, 7, 7, 1, 7, 7, 1, 7, 7, 7, 11, 11, 1, 1, 19, 1, 1, 23, 11, 17, 1, 11, 1, 1, 11, 17, 29, 1, 1, 13, 1, 13, 1, 29, 11, 29, 1, 13, 1, 11, 11, 1, 1, 17, 1, 13, 17, 29, 1, 47, 13, 1, 13, 19, 17, 29, 1, 17, 59, 1, 1, 29, 1, 41, 29, 1, 1

Offset: 1

Author

Dmitry Kamenetsky, Dec 29 2010 Robert Gerbicz, Dec 29 2010

Keywords

• nonn
• tabl

Comments

Conjecture: for every n>1 and 1<=k<=n there is a prime in the interval [k*n!+1, k*n!+3*n*log(n)^2]. [Robert Gerbicz, Dec 28 2010]

Examples

			Triangle begins:
1
1,1
1,1,1
5,5,1,1
7,1,7,7,1
7,7,1,7,7,7
11,11,1,1,19,1,1
23,11,17,1,11,1,1,11
17,29,1,1,13,1,13,1,29
11,29,1,13,1,11,11,1,1,17
1,13,17,29,1,47,13,1,13,19,17
29,1,17,59,1,1,29,1,41,29,1,1
		

Programs

Mathematica

Flatten[Table[NextPrime[k*n!] - k*n!, {n, 12}, {k, n}]]