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

Author

Muniru A Asiru, Feb 04 2019

Keywords

• nonn
• tabf

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.

Examples

			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;
  ...
		

Links

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

Crossrefs

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

Cf. A000040.

Programs

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);

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 *)