login
The OEIS is supported by the many generous donors to the OEIS Foundation.

 

Logo
Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A124223 Table T(n,k) = reciprocal of k modulo prime(n), for 1 <= k < prime(n). 5
1, 1, 2, 1, 3, 2, 4, 1, 4, 5, 2, 3, 6, 1, 6, 4, 3, 9, 2, 8, 7, 5, 10, 1, 7, 9, 10, 8, 11, 2, 5, 3, 4, 6, 12, 1, 9, 6, 13, 7, 3, 5, 15, 2, 12, 14, 10, 4, 11, 8, 16, 1, 10, 13, 5, 4, 16, 11, 12, 17, 2, 7, 8, 3, 15, 14, 6, 9, 18, 1, 12, 8, 6, 14, 4, 10, 3, 18, 7, 21, 2, 16, 5, 20, 13, 19, 9, 17, 15, 11, 22 (list; graph; refs; listen; history; text; internal format)
OFFSET
1,3
COMMENTS
T(n,k) = smallest m such that k*m == 1 (mod prime(n)); prime(n) is the n-th prime: A000040(n).
LINKS
Eric Weisstein's World of Mathematics, Modular Inverse
FORMULA
From Alexander Elkins (alexander_elkins(AT)hotmail.com), Mar 26 2010: (Start)
T(n, 1) = 1;
T(n, T(n,k)) = k;
T(n, prime(n)-1) = prime(n)-1. (End)
T(n,k) = k^(prime(n)-2) mod prime(n), with 1 <= k < prime(n). - Ridouane Oudra, Oct 04 2022
EXAMPLE
From Alexander Elkins (alexander_elkins(AT)hotmail.com), Mar 26 2010: (Start)
Table begins:
1;
1,2;
1,3,2,4;
1,4,5,2,3,6;
1,6,4,3,9,2,8,7,5,10;
1,7,9,10,8,11,2,5,3,4,6,12;
1,9,6,13,7,3,5,15,2,12,14,10,4,11,8,16;
1,10,13,5,4,16,11,12,17,2,7,8,3,15,14,6,9,18;
1,12,8,6,14,4,10,3,18,7,21,2,16,5,20,13,19,9,17,15,11,22;
... (End)
MAPLE
seq(seq(k^(ithprime(n)-2) mod ithprime(n), k=1..ithprime(n)-1), n=1..12); # Ridouane Oudra, Oct 04 2022
MATHEMATICA
Flatten[Table[PowerMod[n, -1, p], {p, Prime[Range[9]]}, {n, p-1}]] (* Alexander Elkins (alexander_elkins(AT)hotmail.com), Mar 26 2010 *)
T[n_, k_] := ModularInverse[k, Prime[n]]; Table[T[n, k], {n, 1, 9}, {k, 1, Prime[n]-1}] // Flatten (* Jean-François Alcover, May 08 2017 *)
PROG
(PARI) row(n) = my(p=prime(n)); vector(p-1, k, lift(1/Mod(k, prime(n)))); \\ Michel Marcus, Feb 24 2023
CROSSREFS
Cf. A124224, A102057, A000040, A006093 (row lengths).
Sequence in context: A003963 A003960 A243499 * A295908 A300980 A260429
KEYWORD
nonn,tabf
AUTHOR
STATUS
approved

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

License Agreements, Terms of Use, Privacy Policy. .

Last modified March 28 22:04 EDT 2024. Contains 371254 sequences. (Running on oeis4.)