A323874 - OEIS

A323874

Irregular triangle of 13^k mod prime(n).

1, 1, 1, 3, 4, 2, 1, 6, 1, 2, 4, 8, 5, 10, 9, 7, 3, 6, 0, 1, 13, 16, 4, 1, 13, 17, 12, 4, 14, 11, 10, 16, 18, 6, 2, 7, 15, 5, 8, 9, 3, 1, 13, 8, 12, 18, 4, 6, 9, 2, 3, 16, 1, 13, 24, 22, 25, 6, 20, 28, 16, 5, 7, 4, 23, 9, 1, 13, 14, 27, 10, 6, 16, 22, 7, 29, 5

(list; graph; refs; listen; history; text; internal format)

OFFSET

1,4

COMMENTS

Length of the n-th row (n != 6) is the order of 13 modulo the n-th prime.

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

LINKS

Table of n, a(n) for n=1..77.

EXAMPLE

The first 10 rows are:

1, 3, 4, 2

1, 6

1, 2, 4, 8, 5, 10, 9, 7, 3, 6

1, 13, 16, 4

1, 13, 17, 12, 4, 14, 11, 10, 16, 18, 6, 2, 7, 15, 5, 8, 9, 3

1, 13, 8, 12, 18, 4, 6, 9, 2, 3, 16

1, 13, 24, 22, 25, 6, 20, 28, 16, 5, 7, 4, 23, 9

MAPLE

T:= n-> (p-> `if`(p=13, 0, seq(13&^k mod p,

k=0..numtheory[order](13, p)-1)))(ithprime(n)):

seq(T(n), n=1..15); # Alois P. Heinz, Feb 06 2019

MATHEMATICA

With[{q = 13}, Table[If[p == q, {0}, Array[PowerMod[q, #, p] &, MultiplicativeOrder[q, p], 0]], {p, Prime@ Range@ 11}]] // Flatten (* Michael De Vlieger, Feb 25 2019 *)

PROG

(GAP) A000040:=Filtered([1..350], IsPrime);; p:=6;;

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. A000040.

Cf. A201908 (2^k), A201909 (3^k), A201910 (5^k), A201911 (7^k), A323873 (11^k), this sequence (13^k).

Sequence in context: A303869 A081246 A264928 * A326765 A096411 A228340

Adjacent sequences: A323871 A323872 A323873 * A323875 A323876 A323877

KEYWORD

nonn,tabf

AUTHOR

Muniru A Asiru, Feb 04 2019

STATUS

approved