|
%I #13 Sep 17 2021 18:28:57
%S 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,
%T 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,
%U 29,1,47,13,1,13,19,17,29,1,17,59,1,1,29,1,41,29,1,1
%N Triangular array a(n,k) read by rows: nextprime(k*n!)-k*n!. For 1<=k<=n.
%C 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]
%e Triangle begins:
%e 1
%e 1,1
%e 1,1,1
%e 5,5,1,1
%e 7,1,7,7,1
%e 7,7,1,7,7,7
%e 11,11,1,1,19,1,1
%e 23,11,17,1,11,1,1,11
%e 17,29,1,1,13,1,13,1,29
%e 11,29,1,13,1,11,11,1,1,17
%e 1,13,17,29,1,47,13,1,13,19,17
%e 29,1,17,59,1,1,29,1,41,29,1,1
%t Flatten[Table[NextPrime[k*n!] - k*n!, {n, 12}, {k, n}]]
%K nonn,tabl
%O 1,7
%A _Dmitry Kamenetsky_, Dec 29 2010 _Robert Gerbicz_, Dec 29 2010
|
