A168399 -id:A168399 - cp's OEIS frontend

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

T. D. Noe, Dec 07 2011

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).

			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

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

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).

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

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]]}]]

A271350 a(n) = 3^n mod 83.

Original entry on oeis.org

1, 3, 9, 27, 81, 77, 65, 29, 4, 12, 36, 25, 75, 59, 11, 33, 16, 48, 61, 17, 51, 70, 44, 49, 64, 26, 78, 68, 38, 31, 10, 30, 7, 21, 63, 23, 69, 41, 40, 37, 28, 1, 3, 9, 27, 81, 77, 65, 29, 4, 12, 36, 25, 75, 59, 11, 33, 16, 48, 61, 17, 51, 70, 44, 49, 64, 26

Offset: 0

Vincenzo Librandi, Apr 05 2016

Vincenzo Librandi, Table of n, a(n) for n = 0..1000
Index entries for linear recurrences with constant coefficients, signature (0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1).

Cf. similar sequences of the type 3^n mod p, where p is a prime: 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), this sequence (83), A036136 (89), A036142 (113), A036143 (127), A271351 (131), A036145 (137), A036158 (199), A271352 (211), A036160 (223).

Magma
```
[Modexp(3, n, 83): n in [0..100]];
```
Mathematica
```
PowerMod[3, Range[0, 100], 83]
```

a(n) = lift(Mod(3, 83)^n); \\ Altug Alkan, Apr 05 2016

a(n) = a(n-41).

cp's OEIS Frontend

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

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