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A268491 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.

%I A268491 #37 Dec 23 2024 14:53:44
%S A268491 2,8,3,68,33,5,1118,348,40,7,2273,2273,271,128,11,197468,27298,10281,
%T A268491 557,115,13,1728998,112383,112383,20005,3209,302,17,1728998,1728998,
%U A268491 1728998,666651,87189,5470,226,19,447914738,447914738,16601856,16601856,2598191
%N A268491 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 A268491 R. J. Mathar, in reply to Zak Seidov, <a href="https://web.archive.org/web/*/http://list.seqfan.eu/oldermail/seqfan/2016-April/016277.html">11 related sequences</a>, SeqFan list, Apr 14 2016.
%e A268491 The array reads: (See the original post on the SeqFan list for more data.)
%e A268491    n\k: 1       2        3        4        5          6          7          8
%e A268491    1    2,      3,       5,       7,       11,       13,        17,        19, ...
%e A268491    2    8,      33,     40,      128,      115,     302,        226,       226, ...
%e A268491    3   68,     348,     271,     557,     3209,     5470,       226,      6229, ...
%e A268491    4  1118,    2273,   10281,   20005,    87189,   12899,      88937,    709247 ...
%e A268491    5  2273,   27298,  112383,  666651,   2598191,  874663,    9124786,  3004394 ...
%e A268491    6 197468, 112383, 1728998, 16601856, 81018715, 154484096, 285307475, 34371403...
%p A268491 T := proc(n,k)
%p A268491     local lrem,leval,i ;
%p A268491     lrem := [] ;
%p A268491     leval := [] ;
%p A268491     for i from k to n+k-1 do
%p A268491         lrem := [op(lrem),ithprime(i+1)] ;
%p A268491         leval := [op(leval),ithprime(i)] ;
%p A268491     end do:
%p A268491     chrem(leval,lrem) ;
%p A268491 end proc:
%p A268491 seq(seq(T(d-k,k),k=1..d-1),d=2..12) ; # _R. J. Mathar_, Apr 14 2016
%o A268491 (PARI) T(n,k)=lift(chinese(vector(n,i,Mod(prime(k+i-1),prime(k+i)))))
%o A268491 concat(vector(10,n,vector(n,j, T(n-j+1,j))))
%Y A268491 A157752 is column k=1. -  _R. J. Mathar_, Apr 14 2016
%Y A268491 The first terms of A319524 are the first terms of line n=2. - _Alexandra Hercilia Pereira Silva_, Sep 19 2020.
%K A268491 nonn,tabl
%O A268491 1,1
%A A268491 _M. F. Hasler_, Apr 14 2016