A323873 Irregular triangle of 11^k mod prime(n).

1, 1, 2, 1, 1, 4, 2, 0, 1, 11, 4, 5, 3, 7, 12, 2, 9, 8, 10, 6, 1, 11, 2, 5, 4, 10, 8, 3, 16, 6, 15, 12, 13, 7, 9, 14, 1, 11, 7, 1, 11, 6, 20, 13, 5, 9, 7, 8, 19, 2, 22, 12, 17, 3, 10, 18, 14, 16, 15, 4, 21, 1, 11, 5, 26, 25, 14, 9, 12, 16, 2, 22, 10, 23, 21, 28

Offset

1,3

Comments

Length of the n-th row (n != 5) is the order of 11 modulo the n-th prime.

Except for the fifth row, the first term of each row is 1.

Links

Alois P. Heinz, Rows n = 1..120, flattened

Example

The first 9 rows are:
  1;
  1,  2;
  1;
  1,  4, 2;
  0;
  1, 11, 4,  5,  3,  7, 12, 2,  9,  8, 10,  6;
  1, 11, 2,  5,  4, 10,  8, 3, 16,  6, 15, 12, 13,  7, 9, 14;
  1, 11, 7;
  1, 11, 6, 20, 13,  5,  9, 7,  8, 19,  2, 22, 12, 17, 3, 10, 18, 14, 16, 15, 4, 21;
  ...

Maple

T:= n-> (p-> `if`(p=11, 0, seq(11&^k mod p,
         k=0..numtheory[order](11, p)-1)))(ithprime(n)):
seq(T(n), n=1..15);  # Alois P. Heinz, Feb 06 2019

Mathematica

Table[If[p == 11, {0}, Array[PowerMod[11, #, p] &, MultiplicativeOrder[11, p], 0]], {p, Prime@ Range@ 10}] (* Michael De Vlieger, Feb 25 2019 *)

Prog

(GAP) A000040:=Filtered([1..350], IsPrime);; p:=5;;
R:=List([1..Length(A000040)], n->OrderMod(A000040[p], A000040[n]));;
a1:=List([1..p-1], n->List([0..R[n]-1], k->PowerMod(A000040[p], k, A000040[n])));;
a:=Flat(Concatenation(a1, [0], List([p+1..2*p], n->List([0..R[n]-1], k->PowerMod(A000040[p], k, A000040[n])))));; Print(a);

Crossrefs

Cf. A201908 (2^k), A201909 (3^k), A201910 (5^k), A201911 (7^k), this sequence (11^k), A323874 (13^k).

Cf. A000040.

Sequence in context: A124939 A187800 A340189 * A365582 A367559 A099020

Adjacent sequences: A323870 A323871 A323872 * A323874 A323875 A323876

Keyword

nonn,tabf

Author

Muniru A Asiru, Feb 04 2019

Status

approved