login
The OEIS Foundation is supported by donations from users of the OEIS and by a grant from the Simons Foundation.

 

Logo


Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A323376 Square array read by ascending antidiagonals: T(n,k) is the multiplicative order of the n-th prime modulo the k-th prime, or 0 if n = k, n >= 1, k >= 1. 1
0, 1, 2, 1, 0, 4, 1, 2, 4, 3, 1, 1, 0, 6, 10, 1, 2, 4, 6, 5, 12, 1, 1, 1, 0, 5, 3, 8, 1, 2, 4, 3, 10, 4, 16, 18, 1, 1, 4, 2, 0, 12, 16, 18, 11, 1, 2, 2, 6, 10, 12, 16, 9, 11, 28, 1, 2, 4, 6, 10, 0, 16, 3, 22, 28, 5, 1, 1, 2, 3, 10, 6, 4, 3, 22, 14, 30, 36 (list; table; graph; refs; listen; history; text; internal format)
OFFSET

1,3

COMMENTS

The maximum element in the k-th column is prime(k) - 1. By Dirichlet's theorem on arithmetic progressions, all divisors of prime(k) - 1 occur infinitely many times in the n-th column.

LINKS

Alois P. Heinz, Antidiagonals n = 1..200, flattened

FORMULA

T(n,k) = A250211(prime(n), prime(k)).

EXAMPLE

Table begins

     |  k  | 1  2  3  4   5   6   7   8   9  10  ...

   n | p() | 2  3  5  7  11  13  17  19  23  29  ...

  ---+-----+----------------------------------------

   1 |   2 | 0, 2, 4, 3, 10, 12,  8, 18, 11, 28, ...

   2 |   3 | 1, 0, 4, 6,  5,  3, 16, 18, 11, 28, ...

   3 |   5 | 1, 2, 0, 6,  5,  4, 16,  9, 22, 14, ...

   4 |   7 | 1, 1, 4, 0, 10, 12, 16,  3, 22,  7, ...

   5 |  11 | 1, 2, 1, 3,  0, 12, 16,  3, 22, 28, ...

   6 |  13 | 1, 1, 4, 2, 10,  0,  4, 18, 11, 14, ...

   7 |  17 | 1, 2, 4, 6, 10,  6,  0,  9, 22,  4, ...

   8 |  19 | 1, 1, 2, 6, 10, 12,  8,  0, 22, 28, ...

   9 |  23 | 1, 2, 4, 3,  1,  6, 16,  9 , 0,  7, ...

  10 |  29 | 1, 2, 2, 1, 10,  3, 16, 18, 11,  0, ...

  ...

MAPLE

A:= (n, k)-> `if`(n=k, 0, (p-> numtheory[order](p(n), p(k)))(ithprime)):

seq(seq(A(1+d-k, k), k=1..d), d=1..14);  # Alois P. Heinz, Feb 06 2019

MATHEMATICA

T[n_, k_] := If[n == k, 0, MultiplicativeOrder[Prime[n], Prime[k]]]; Table[T[n, k], {n, 1, 10}, {k, 1, 10}] (* Peter Luschny, Jan 20 2019 *)

PROG

(PARI) T(n, k) = if(n==k, 0, znorder(Mod(prime(n), prime(k))))

CROSSREFS

Cf. A250211.

Cf. A014664 (1st row), A062117 (2nd row), A211241 (3rd row), A211243 (4th row), A039701 (2nd column).

Cf. A226367 (lower diagonal), A226295 (upper diagonal).

Sequence in context: A334044 A143724 A143425 * A166555 A136329 A122073

Adjacent sequences:  A323373 A323374 A323375 * A323377 A323378 A323379

KEYWORD

nonn,tabl

AUTHOR

Jianing Song, Jan 12 2019

STATUS

approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recent
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy. .

Last modified September 26 20:36 EDT 2020. Contains 337374 sequences. (Running on oeis4.)