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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.
0
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
1,1
LINKS
R. J. Mathar, in reply to Zak Seidov, 11 related sequences, SeqFan list, Apr 14 2016.
EXAMPLE
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...
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
PROG
(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))))
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.
Sequence in context: A282637 A256411 A218609 * A076588 A068565 A092042
KEYWORD
nonn,tabl
AUTHOR
M. F. Hasler, Apr 14 2016
STATUS
approved