A059256 -id:A059256 - cp's OEIS frontend

A049561 Primes p such that x^29 = 2 has a solution mod p.

2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47, 53, 61, 67, 71, 73, 79, 83, 89, 97, 101, 103, 107, 109, 113, 127, 131, 137, 139, 149, 151, 157, 163, 167, 173, 179, 181, 191, 193, 197, 199, 211, 223, 227, 229, 239, 241, 251, 257, 263, 269, 271, 277, 281

Offset: 1

N. J. A. Sloane

Complement of A059256 relative to A000040. - Vincenzo Librandi, Sep 14 2012

			0^29 == 2 (mod 2). 2^29 == 2 (mod 3). 2^29 == 2 (mod 5). 4^29 == 2 (mod 7). 6^29 == 2 (mod 11). 6^29 == 2 (mod 13). 15^29 == 2 (mod 17). 13^29 == 2 (mod 19). 3^29 == 2 (mod 23). 2^29 == 2 (mod 29). 16^29 == 2 (mod 31). 32^29 == 2 (mod 37). 20^29 == 2 (mod 41). 2^29 == 2 (mod 43). - _R. J. Mathar_, Jul 20 2025

R. J. Mathar, Table of n, a(n) for n = 1..1000
Index entries for related sequences

Cf. A000040, A059256.

[p: p in PrimesUpTo(300) | exists(t){x : x in ResidueClassRing(p) | x^29 eq 2}]; // Vincenzo Librandi, Sep 14 2012

ok[p_]:= Reduce[Mod[x^29 - 2, p] == 0, x, Integers] =!= False; Select[Prime[Range[100]], ok] (* Vincenzo Librandi, Sep 14 2012 *)

A248572 a(n) = 29*n + 1.

Original entry on oeis.org

1, 30, 59, 88, 117, 146, 175, 204, 233, 262, 291, 320, 349, 378, 407, 436, 465, 494, 523, 552, 581, 610, 639, 668, 697, 726, 755, 784, 813, 842, 871, 900, 929, 958, 987, 1016, 1045, 1074, 1103, 1132, 1161, 1190, 1219, 1248, 1277, 1306, 1335, 1364, 1393, 1422

Offset: 0

Karl V. Keller, Jr., Oct 08 2014

Numbers congruent to 1 mod 29.

Both A141977 and A059256 give the primes in this sequence.

			For n = 5, 29n + 1 = 145 + 1 = 146.

Karl V. Keller, Jr., Table of n, a(n) for n = 0..10000
Index entries for linear recurrences with constant coefficients, signature (2,-1).

Cf. A141977 (Primes congruent to 1 mod 29).
Cf. A059256 (Primes p such that x^29 = 2 has no solution mod p).
Cf. A195819 (multiples of 29).

List([0..60], n-> 29*n+1); # G. C. Greubel, May 24 2019

[29*n+1: n in [0..60]]; // Vincenzo Librandi, Oct 26 2014

29Range[0, 60] + 1 (* Alonso del Arte, Oct 09 2014 *)
CoefficientList[Series[(1+28x)/(1-x)^2, {x, 0, 60}], x] (* Vincenzo Librandi, Oct 26 2014 *)
LinearRecurrence[{2,-1},{1,30},50] (* Harvey P. Dale, Oct 08 2019 *)

vector(60, n, n--; 29*n+1) \\ Derek Orr, Oct 08 2014

for n in range(61):
    print(29*n+1, end=', ')

[29*n+1 for n in (0..60)] # G. C. Greubel, May 24 2019

a(n) = 29*n + 1.
G.f.: (1+28*x)/(1-x)^2. - Vincenzo Librandi, Oct 26 2014 [corrected by Georg Fischer, May 24 2019]
E.g.f.: (1 + 29*x)*exp(x). - G. C. Greubel, May 24 2019

cp's OEIS Frontend

A049561 Primes p such that x^29 = 2 has a solution mod p.

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