A201909 Irregular triangle of 3^k mod prime(n).

1, 0, 1, 3, 4, 2, 1, 3, 2, 6, 4, 5, 1, 3, 9, 5, 4, 1, 3, 9, 1, 3, 9, 10, 13, 5, 15, 11, 16, 14, 8, 7, 4, 12, 2, 6, 1, 3, 9, 8, 5, 15, 7, 2, 6, 18, 16, 10, 11, 14, 4, 12, 17, 13, 1, 3, 9, 4, 12, 13, 16, 2, 6, 18, 8, 1, 3, 9, 27, 23, 11, 4, 12, 7, 21, 5, 15

Offset

1,4

Comments

The row lengths are in A062117. Except for the second row, the first term of each row is 1. Many sequences are in this one: starting at A036119 (mod 17) and A070341 (mod 11).

Links

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

Example

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

Mathematica

nn = 10; p = 3; 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(7, P[n]));;
Flat(Concatenation([1, 1, 1, 2, 4, 3, 0], List([5..10], n->List([0..R[n]-1], k->PowerMod(7, k, P[n]))))); # Muniru A Asiru, Feb 01 2019

Crossrefs

Cf. A062117, A201908 (2^k), A201910 (5^k), A201911 (7^k).

Cf. A070352 (5), A033940 (7), A070341 (11), A168399 (13), A036119 (17), A070342 (19), A070356 (23), A070344 (29), A036123 (31), A070346 (37), A070361 (41), A036126 (43), A070364 (47), A036134 (79), A036136 (89), A036142 (113), A036143 (127), A036145 (137), A036158 (199), A036160 (223).

Sequence in context: A105825 A238570 A145425 * A070352 A227216 A239678

Adjacent sequences: A201906 A201907 A201908 * A201910 A201911 A201912

Keyword

nonn,tabf

Author

T. D. Noe, Dec 07 2011

Status

approved