|
%I #36 May 28 2023 08:46:25
%S 2,8,3,68,33,5,1118,348,40,7,2273,2273,271,128,11,197468,27298,10281,
%T 557,115,13,1728998,112383,112383,20005,3209,302,17,1728998,1728998,
%U 1728998,666651,87189,5470,226,19,447914738,447914738,16601856,16601856,2598191
%N Array T(n,k) = least integer congruent to prime(i) mod prime(i+1) for all k <= i <= k+n; n, k >= 1; read by upward diagonals.
%H R. J. Mathar, in reply to Zak Seidov, <a href="http://list.seqfan.eu/oldermail/seqfan/2016-April/016277.html">11 related sequences</a>, SeqFan list, Apr 14 2016.
%e The array reads: (See the original post on the SeqFan list for more data.)
%e n\k: 1 2 3 4 5 6 7 8
%e 1 2, 3, 5, 7, 11, 13, 17, 19, ...
%e 2 8, 33, 40, 128, 115, 302, 226, 226, ...
%e 3 68, 348, 271, 557, 3209, 5470, 226, 6229, ...
%e 4 1118, 2273, 10281, 20005, 87189, 12899, 88937, 709247 ...
%e 5 2273, 27298, 112383, 666651, 2598191, 874663, 9124786, 3004394 ...
%e 6 197468, 112383, 1728998, 16601856, 81018715, 154484096, 285307475, 34371403...
%p T := proc(n,k)
%p local lrem,leval,i ;
%p lrem := [] ;
%p leval := [] ;
%p for i from k to n+k-1 do
%p lrem := [op(lrem),ithprime(i+1)] ;
%p leval := [op(leval),ithprime(i)] ;
%p end do:
%p chrem(leval,lrem) ;
%p end proc:
%p seq(seq(T(d-k,k),k=1..d-1),d=2..12) ; # _R. J. Mathar_, Apr 14 2016
%o (PARI) T(n,k)=lift(chinese(vector(n,i,Mod(prime(k+i-1),prime(k+i)))))
%o concat(vector(10,n,vector(n,j, T(n-j+1,j))))
%Y A157752 is column k=1. - _R. J. Mathar_, Apr 14 2016
%Y The first terms of A319524 are the first terms of line n=2. - _Alexandra Hercilia Pereira Silva_, Sep 19 2020.
%K nonn,tabl
%O 1,1
%A _M. F. Hasler_, Apr 14 2016
|
