A201910 Irregular triangle of 5^k mod prime(n).

1, 1, 2, 0, 1, 5, 4, 6, 2, 3, 1, 5, 3, 4, 9, 1, 5, 12, 8, 1, 5, 8, 6, 13, 14, 2, 10, 16, 12, 9, 11, 4, 3, 15, 7, 1, 5, 6, 11, 17, 9, 7, 16, 4, 1, 5, 2, 10, 4, 20, 8, 17, 16, 11, 9, 22, 18, 21, 13, 19, 3, 15, 6, 7, 12, 14, 1, 5, 25, 9, 16, 22, 23, 28, 24, 4

Offset

1,3

Comments

Except for the third row, the first term of each row is 1. Many sequences are in this one: starting at A036121 (mod 23) and A070365 (mod 7).

Links

T. D. Noe, Rows n = 1..60, flattened

Example

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

Mathematica

nn = 10; p = 5; t = p^Range[0, Prime[nn]]; Flatten[Table[If[Mod[n, p] == 0, {0}, tm = Mod[t, n]; len = Position[tm, 1, 1, 2][[-1, 1]]; Take[tm, len-1]], {n, Prime[Range[nn]]}]]

Prog

(GAP) P:=Filtered([1..350], IsPrime);;
R:=List([1..Length(P)], n->OrderMod(5, P[n]));;
Flat(Concatenation([1, 1, 2, 0], List([3..10], n->List([0..R[n]-1], k->PowerMod(5, k, P[n]))))); # Muniru A Asiru, Feb 02 2019

Crossrefs

Cf. A201908 (2^k), A201909 (3^k), A201911 (7^k).

Cf. A070365 (7), A070367 (11), A070368 (13), A070371 (17), A070373 (19), A036121 (23), A070379 (29), A070384 (37), A070387 (41), A070389 (43), A036127 (47), A036133 (73), A036137 (97), A036139 (103), A036149 (157), A036151 (167), A036156 (193).

Sequence in context: A197808 A085650 A343751 * A109450 A086810 A085838

Adjacent sequences: A201907 A201908 A201909 * A201911 A201912 A201913

Keyword

nonn,tabf

Author

T. D. Noe, Dec 07 2011

Status

approved