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 A178916 Triangular array a(n,k) read by rows: nextprime(k*n!)-k*n!. For 1<=k<=n. 0
 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 (list; table; graph; refs; listen; history; text; internal format)
 OFFSET 1,7 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]. [From Robert Gerbicz, Dec 28 2010] LINKS EXAMPLE 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 MATHEMATICA Flatten[Table[NextPrime[k*n!] - k*n!, {n, 12}, {k, n}]] CROSSREFS Sequence in context: A046599 A100285 A172355 * A046568 A046571 A172349 Adjacent sequences:  A178913 A178914 A178915 * A178917 A178918 A178919 KEYWORD nonn,tabl AUTHOR Dmitry Kamenetsky, Dec 29 2010 Robert Gerbicz, Dec 29 2010 STATUS approved

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