A323874 -id:A323874 - cp's OEIS frontend

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

Muniru A Asiru, Feb 04 2019

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.

			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;
  ...

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

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

Cf. A000040.

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);

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

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

cp's OEIS Frontend

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

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