A201911 Irregular triangle of 7^k mod prime(n).

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

Offset

1,4

Comments

Except for the fourth row, the first term of each row is 1. Many sequences are in this one: starting at A036132 (mod 71) and A070404 (mod 11).

Links

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

Example

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

Mathematica

nn = 10; p = 7; 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. A201908 (2^k), A201909 (3^k), A201910 (5^k).

Cf. A070404 (11), A070405 (13), A070407 (17), A070409 (23), A070413 (29), A070415 (31), A070420 (37), A070422 (39), A070424 (41), A070425 (43), A070429 (47), A036132 (71).

Sequence in context: A121819 A134138 A351427 * A048644 A246713 A106137

Adjacent sequences: A201908 A201909 A201910 * A201912 A201913 A201914

Keyword

nonn,tabf

Author

T. D. Noe, Dec 07 2011

Status

approved