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

%I A323873 #24 Oct 23 2019 21:53:36
%S A323873 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,
%T A323873 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,
%U A323873 15,4,21,1,11,5,26,25,14,9,12,16,2,22,10,23,21,28
%N A323873 Irregular triangle of 11^k mod prime(n).
%C A323873 Length of the n-th row (n != 5) is the order of 11 modulo the n-th prime.
%C A323873 Except for the fifth row, the first term of each row is 1.
%H A323873 Alois P. Heinz, <a href="/A323873/b323873.txt">Rows n = 1..120, flattened</a>
%e A323873 The first 9 rows are:
%e A323873   1;
%e A323873   1,  2;
%e A323873   1;
%e A323873   1,  4, 2;
%e A323873   0;
%e A323873   1, 11, 4,  5,  3,  7, 12, 2,  9,  8, 10,  6;
%e A323873   1, 11, 2,  5,  4, 10,  8, 3, 16,  6, 15, 12, 13,  7, 9, 14;
%e A323873   1, 11, 7;
%e A323873   1, 11, 6, 20, 13,  5,  9, 7,  8, 19,  2, 22, 12, 17, 3, 10, 18, 14, 16, 15, 4, 21;
%e A323873   ...
%p A323873 T:= n-> (p-> `if`(p=11, 0, seq(11&^k mod p,
%p A323873          k=0..numtheory[order](11, p)-1)))(ithprime(n)):
%p A323873 seq(T(n), n=1..15);  # _Alois P. Heinz_, Feb 06 2019
%t A323873 Table[If[p == 11, {0}, Array[PowerMod[11, #, p] &, MultiplicativeOrder[11, p], 0]], {p, Prime@ Range@ 10}] (* _Michael De Vlieger_, Feb 25 2019 *)
%o A323873 (GAP) A000040:=Filtered([1..350],IsPrime);; p:=5;;
%o A323873 R:=List([1..Length(A000040)],n->OrderMod(A000040[p],A000040[n]));;
%o A323873 a1:=List([1..p-1],n->List([0..R[n]-1],k->PowerMod(A000040[p],k,A000040[n])));;
%o A323873 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);
%Y A323873 Cf. A201908 (2^k), A201909 (3^k), A201910 (5^k), A201911 (7^k), this sequence (11^k), A323874 (13^k).
%Y A323873 Cf. A000040.
%K A323873 nonn,tabf
%O A323873 1,3
%A A323873 _Muniru A Asiru_, Feb 04 2019