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.
2, 8, 3, 68, 33, 5, 1118, 348, 40, 7, 2273, 2273, 271, 128, 11, 197468, 27298, 10281, 557, 115, 13, 1728998, 112383, 112383, 20005, 3209, 302, 17, 1728998, 1728998, 1728998, 666651, 87189, 5470, 226, 19, 447914738, 447914738, 16601856, 16601856, 2598191
Offset: 1
Examples
The array reads: (See the original post on the SeqFan list for more data.) n\k: 1 2 3 4 5 6 7 8 1 2, 3, 5, 7, 11, 13, 17, 19, ... 2 8, 33, 40, 128, 115, 302, 226, 226, ... 3 68, 348, 271, 557, 3209, 5470, 226, 6229, ... 4 1118, 2273, 10281, 20005, 87189, 12899, 88937, 709247 ... 5 2273, 27298, 112383, 666651, 2598191, 874663, 9124786, 3004394 ... 6 197468, 112383, 1728998, 16601856, 81018715, 154484096, 285307475, 34371403...
Links
- R. J. Mathar, in reply to Zak Seidov, 11 related sequences, SeqFan list, Apr 14 2016.
Crossrefs
A157752 is column k=1. - R. J. Mathar, Apr 14 2016
The first terms of A319524 are the first terms of line n=2. - Alexandra Hercilia Pereira Silva, Sep 19 2020.
Programs
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Maple
T := proc(n,k) local lrem,leval,i ; lrem := [] ; leval := [] ; for i from k to n+k-1 do lrem := [op(lrem),ithprime(i+1)] ; leval := [op(leval),ithprime(i)] ; end do: chrem(leval,lrem) ; end proc: seq(seq(T(d-k,k),k=1..d-1),d=2..12) ; # R. J. Mathar, Apr 14 2016 -
PARI
T(n,k)=lift(chinese(vector(n,i,Mod(prime(k+i-1),prime(k+i))))) concat(vector(10,n,vector(n,j, T(n-j+1,j))))