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

1,1

Links

Table of n, a(n) for n=1..41.

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

Adjacent sequences: A268488 A268489 A268490 * A268492 A268493 A268494

Keyword

nonn,tabl

Author

M. F. Hasler, Apr 14 2016

Status

approved