A070341 -id:A070341 - 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]]}]]

A010691 Period 2: repeat (1,10).

Original entry on oeis.org

1, 10, 1, 10, 1, 10, 1, 10, 1, 10, 1, 10, 1, 10, 1, 10, 1, 10, 1, 10, 1, 10, 1, 10, 1, 10, 1, 10, 1, 10, 1, 10, 1, 10, 1, 10, 1, 10, 1, 10, 1, 10, 1, 10, 1, 10, 1, 10, 1, 10, 1, 10, 1, 10, 1, 10, 1, 10, 1, 10, 1, 10, 1, 10, 1, 10

Offset: 0

N. J. A. Sloane

Regular continued fraction of (5+sqrt 35)/10. - R. J. Mathar, Nov 21 2011

Sequence is an infinite palindrome in two ways (numbers and English names): ONE, TEN, ONE, TEN, ONE, TEN, ONE, ... . - Eric Angelini, Sep 16 2023

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

Cf. A036117, A070341, A168429, A070367, A070392, A070404, A048271, A187466.

[10^n mod 11: n in [0..80]]; // Vincenzo Librandi, Aug 24 2011

g:=(1+10*z)/((1-z^2)): gser:=series(g, z=0, 66): seq((coeff(gser, z, n)), n=0..65); # Zerinvary Lajos, Feb 25 2009

PadRight[{},100,{1,10}] (* Harvey P. Dale, Aug 27 2013 *)

a(n) = -9/2*(-1)^n + 11/2.
G.f.: (1+10*z)/(1-z^2). - Zerinvary Lajos, Feb 25 2009
a(n) = 10^n mod 11. - M. F. Hasler, Mar 10 2011
From Nicolas Bělohoubek, Nov 11 2021: (Start)
a(n) = 10/a(n-1). See also A010695.
a(n) = 11 - a(n-1). See also A010712. (End)

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).

A187466 a(n) = 9^n mod 11.

Original entry on oeis.org

1, 9, 4, 3, 5, 1, 9, 4, 3, 5, 1, 9, 4, 3, 5, 1, 9, 4, 3, 5, 1, 9, 4, 3, 5, 1, 9, 4, 3, 5, 1, 9, 4, 3, 5, 1, 9, 4, 3, 5, 1, 9, 4, 3, 5, 1, 9, 4, 3, 5, 1, 9, 4, 3, 5, 1, 9, 4, 3, 5, 1, 9, 4, 3, 5, 1, 9, 4, 3, 5, 1, 9, 4, 3, 5, 1, 9, 4, 3, 5, 1, 9, 4, 3, 5, 1

Offset: 0

M. F. Hasler, Mar 10 2011

Period 5: repeat [1, 9, 4, 3, 5].

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

Cf. A010691, A036117, A048271, A070341, A070367, A070392, A070404, A168429.

A187466:=n->9^n mod 11: seq(A187466(n), n=0..100); # Wesley Ivan Hurt, Jun 11 2016

PowerMod[9, Range[0, 100], 11] (* Wesley Ivan Hurt, Jun 11 2016 *)

a(n)=lift(Mod(9,11)^n) \\ Charles R Greathouse IV, Mar 22 2016

G.f.: (5*x^4 + 3*x^3 + 4*x^2 + 9*x + 1)/(1 - x^5). - Chai Wah Wu, Jun 04 2016

a(n) = a(n-5) for n>4. - Wesley Ivan Hurt, Jun 11 2016

cp's OEIS Frontend

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

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A010691 Period 2: repeat (1,10).

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

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A187466 a(n) = 9^n mod 11.

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Maple

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