A059236 -id:A059236 - cp's OEIS frontend

A142199 Primes congruent to 2 mod 41.

2, 43, 617, 863, 1109, 1601, 1847, 2011, 2339, 2503, 2749, 3323, 3733, 4799, 5209, 5701, 5783, 6029, 6521, 7013, 7177, 7669, 8161, 8243, 9227, 9391, 9473, 9719, 9883, 10211, 10457, 10867, 10949, 11113, 11933, 12097, 12343, 12589, 12671, 12917, 13163, 13327

Offset: 1

N. J. A. Sloane, Jul 11 2008

Vincenzo Librandi, Table of n, a(n) for n = 1..1000

Cf. A000040, A059236, A142200, A142201.

[p: p in PrimesUpTo(14000) | p mod 41 eq 2 ]; // Vincenzo Librandi, Aug 23 2012

Select[Range[2,30000,41],PrimeQ] (* Vladimir Joseph Stephan Orlovsky, May 17 2011 *)
Select[Prime[Range[5000]],MemberQ[{2},Mod[#,41]]&] (* Vincenzo Librandi, Aug 23 2012 *)

is(n)=isprime(n) && n%41==2 \\ Charles R Greathouse IV, Jul 01 2016

A142200 Primes congruent to 3 mod 41.

Original entry on oeis.org

3, 167, 331, 577, 659, 823, 1069, 1151, 1889, 2053, 2381, 2791, 3037, 3119, 3529, 4021, 4349, 4513, 4759, 5087, 5333, 5743, 6317, 6481, 6563, 7219, 7547, 7793, 8039, 8941, 9187, 9433, 9679, 10007, 10253, 10499, 10663, 10909, 11483, 12713, 12959, 13451, 13697

Offset: 1

N. J. A. Sloane, Jul 11 2008

Vincenzo Librandi, Table of n, a(n) for n = 1..1000

Cf. A000040, A059236, A142199, A142201.

[p: p in PrimesUpTo(14000) | p mod 41 eq 3 ]; // Vincenzo Librandi, Aug 23 2012

Select[Range[3,30000,41],PrimeQ] (* Vladimir Joseph Stephan Orlovsky, May 17 2011 *)
Select[Prime[Range[5000]],MemberQ[{3},Mod[#,41]]&] (* Vincenzo Librandi, Aug 23 2012 *)

is(n)=isprime(n) && n%41==3 \\ Charles R Greathouse IV, Jul 01 2016

A142201 Primes congruent to 4 mod 41.

Original entry on oeis.org

127, 373, 619, 701, 947, 1193, 1439, 1931, 2341, 2423, 2833, 3079, 3407, 3571, 4391, 4637, 4801, 5867, 6113, 6277, 6359, 7507, 7589, 7753, 8081, 8573, 8737, 8819, 9311, 9721, 9803, 9967, 10459, 11197, 11279, 11443, 11689, 12263, 12919, 13001, 13411, 13903

Offset: 1

N. J. A. Sloane, Jul 11 2008

Vincenzo Librandi, Table of n, a(n) for n = 1..1000

Cf. A000040, A059236, A142199, A142200.

[p: p in PrimesUpTo(14000) | p mod 41 eq 4 ]; // Vincenzo Librandi, Aug 23 2012

Select[Range[4,30000,41],PrimeQ] (* Vladimir Joseph Stephan Orlovsky, May 17 2011 *)
Select[Prime[Range[5000]],MemberQ[{4},Mod[#,41]]&] (* Vincenzo Librandi, Aug 23 2012 *)

is(n)=isprime(n) && n%41==4 \\ Charles R Greathouse IV, Jul 02 2016

a(n) ~ 40n log n. - Charles R Greathouse IV, Jul 02 2016

A049573 Primes p such that x^41 = 2 has a solution mod p.

Original entry on oeis.org

2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47, 53, 59, 61, 67, 71, 73, 79, 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, 233, 239, 241, 251, 257, 263, 269, 271, 277

Offset: 1

N. J. A. Sloane

Differs from A000040: 83 does not occur.

			0^41 == 2 (mod 2). 2^41 == 2 (mod 3). 2^41 == 2 (mod 5). 4^41 == 2 (mod 7). 2^41 == 2 (mod 11). 6^41 == 2 (mod 13). 2^41 == 2 (mod 17). 15^41 == 2 (mod 19). 13^41 == 2 (mod 23). 14^41 == 2 (mod 29). 2^41 == 2 (mod 31). 24^41 == 2 (mod 37). 2^41 == 2 (mod 41). 22^41 == 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, A059236 for primes not in this sequence.

[p: p in PrimesUpTo(300) | exists(t){x : x in ResidueClassRing(p) | x^41 eq 2}]; // Vincenzo Librandi, Sep 14 2012

ok[p_]:= Reduce[Mod[x^41 - 2, p] == 0, x, Integers] =!= False; Select[Prime[Range[100]], ok] (* Vincenzo Librandi, Sep 14 2012 *)

A142204 Primes congruent to 7 mod 41.

Original entry on oeis.org

7, 89, 499, 827, 991, 1237, 1319, 1483, 1811, 2221, 2467, 2549, 2713, 3041, 3533, 3697, 3779, 3943, 4271, 4517, 5009, 5419, 5501, 6977, 7879, 8699, 8863, 9109, 9437, 9601, 9929, 10093, 10667, 10831, 11159, 11897, 12143, 12553, 12799, 13127, 13291, 13537

Offset: 1

N. J. A. Sloane, Jul 11 2008

Vincenzo Librandi, Table of n, a(n) for n = 1..1000

Cf. A000040, A059236, A142199, A142200.

[p: p in PrimesUpTo(14000) | p mod 41 eq 7 ]; // Vincenzo Librandi, Aug 23 2012

Select[Range[7,30000,41],PrimeQ] (* Vladimir Joseph Stephan Orlovsky, May 17 2011 *)
Select[Prime[Range[5000]],MemberQ[{7},Mod[#,41]]&] (* Vincenzo Librandi, Aug 23 2012 *)

is(n)=isprime(n) && n%41==7 \\ Charles R Greathouse IV, Jul 02 2016

a(n) ~ 40n log n. - Charles R Greathouse IV, Jul 02 2016

A142205 Primes congruent to 8 mod 41.

Original entry on oeis.org

131, 541, 787, 1033, 1279, 1361, 1607, 2017, 2099, 2591, 2837, 3001, 3083, 3329, 3739, 3821, 4231, 4723, 4969, 5051, 5297, 5953, 6199, 6691, 7019, 7757, 8167, 8741, 9151, 9397, 9479, 9643, 10463, 10627, 10709, 11119, 11447, 11939, 12841, 12923, 13907, 14071

Offset: 1

N. J. A. Sloane, Jul 11 2008

Vincenzo Librandi, Table of n, a(n) for n = 1..1000

Cf. A000040, A059236, A142199, A142200, A142204.

[p: p in PrimesUpTo(15000) | p mod 41 eq 8 ]; // Vincenzo Librandi, Aug 23 2012

Select[Range[8,30000,41],PrimeQ] (* Vladimir Joseph Stephan Orlovsky, May 17 2011 *)
Select[Prime[Range[5000]],MemberQ[{8},Mod[#,41]]&] (* Vincenzo Librandi, Aug 23 2012 *)

is(n)=isprime(n) && n%41==8 \\ Charles R Greathouse IV, Jul 02 2016

a(n) ~ 40n log n. - Charles R Greathouse IV, Jul 02 2016

A142206 Primes congruent to 9 mod 41.

Original entry on oeis.org

173, 337, 419, 829, 911, 1321, 1567, 2141, 2551, 2633, 2797, 2879, 3371, 3617, 3863, 4027, 4273, 4519, 5011, 5503, 5749, 6323, 6569, 6733, 7307, 7717, 7963, 8209, 8291, 8537, 8783, 9029, 9439, 9521, 9767, 9931, 10177, 10259, 11161, 11243, 11489, 11981

Offset: 1

N. J. A. Sloane, Jul 11 2008

Vincenzo Librandi, Table of n, a(n) for n = 1..1000

Cf. A000040, A059236, A142199, A142200, A142205.

[p: p in PrimesUpTo(15000) | p mod 41 eq 9 ]; // Vincenzo Librandi, Aug 23 2012

Select[Prime[Range[1500]],Mod[#,41]==9&]  (* Harvey P. Dale, Apr 22 2011 *)
Select[Prime[Range[5000]],MemberQ[{9},Mod[#,41]]&] (* Vincenzo Librandi, Aug 23 2012 *)
Select[Range[9,12000,41],PrimeQ] (* Harvey P. Dale, Mar 12 2014 *)

is(n)=isprime(n) && n%41==9 \\ Charles R Greathouse IV, Jul 02 2016

a(n) ~ 40n log n. - Charles R Greathouse IV, Jul 02 2016

A142208 Primes congruent to 11 mod 41.

Original entry on oeis.org

11, 257, 421, 503, 1487, 1733, 1979, 2143, 2389, 2963, 3209, 3373, 3701, 3947, 4111, 4357, 4603, 4931, 5669, 6079, 6571, 6653, 6899, 7309, 7883, 8293, 8539, 8867, 9277, 9769, 9851, 10343, 10589, 10753, 11491, 12721, 12967, 13049, 14033, 14197, 14771

Offset: 1

N. J. A. Sloane, Jul 11 2008

Vincenzo Librandi, Table of n, a(n) for n = 1..1000

Cf. A000040, A059236, A142199, A142200, A142206.

[p: p in PrimesUpTo(16000) | p mod 41 eq 11 ]; // Vincenzo Librandi, Aug 23 2012

Select[Range[11,30000,41],PrimeQ] (* Vladimir Joseph Stephan Orlovsky, May 17 2011 *)
Select[Prime[Range[5000]],MemberQ[{11},Mod[#,41]]&] (* Vincenzo Librandi, Aug 23 2012 *)

is(n)=isprime(n) && n%41==11 \\ Charles R Greathouse IV, Jul 02 2016

a(n) ~ 40n log n. - Charles R Greathouse IV, Jul 02 2016

A142209 Primes congruent to 12 mod 41.

Original entry on oeis.org

53, 463, 709, 1201, 1283, 1447, 1693, 2267, 2677, 3169, 3251, 3907, 3989, 4153, 4481, 4973, 5711, 6121, 6203, 6367, 6449, 7187, 7351, 7433, 8089, 8171, 8581, 8663, 9319, 9811, 10139, 10303, 10631, 11287, 11369, 11779, 12107, 12517, 12763, 13009, 13337

Offset: 1

N. J. A. Sloane, Jul 11 2008

Vincenzo Librandi, Table of n, a(n) for n = 1..1000

Cf. A000040, A059236, A142199, A142200, A142208.

[p: p in PrimesUpTo(16000) | p mod 41 eq 12 ]; // Vincenzo Librandi, Aug 23 2012

Select[Range[12,30000,41],PrimeQ] (* Vladimir Joseph Stephan Orlovsky, May 17 2011 *)
Select[Prime[Range[5000]],MemberQ[{12},Mod[#,41]]&] (* Vincenzo Librandi, Aug 23 2012 *)

is(n)=isprime(n) && n%41==12 \\ Charles R Greathouse IV, Jul 02 2016

a(n) ~ 40n log n. - Charles R Greathouse IV, Jul 02 2016

A142210 Primes congruent to 13 mod 41.

Original entry on oeis.org

13, 587, 751, 997, 1489, 1571, 2063, 2309, 2473, 2719, 2801, 3457, 3539, 4441, 4523, 4933, 5179, 5261, 5507, 6163, 6491, 6737, 6983, 7229, 7393, 7639, 8377, 8623, 8951, 9689, 10099, 10181, 10427, 10837, 11083, 11329, 11411, 11657, 11821, 11903, 12149

Offset: 1

N. J. A. Sloane, Jul 11 2008

Vincenzo Librandi, Table of n, a(n) for n = 1..1000

Cf. A000040, A059236, A142199, A142200, A142209.

[p: p in PrimesUpTo(16000) | p mod 41 eq 13 ]; // Vincenzo Librandi, Aug 23 2012

Select[Range[13,30000,41],PrimeQ] (* Vladimir Joseph Stephan Orlovsky, May 17 2011 *)
Select[Prime[Range[5000]],MemberQ[{13},Mod[#,41]]&] (* Vincenzo Librandi, Aug 23 2012 *)

is(n)=isprime(n) && n%41==13 \\ Charles R Greathouse IV, Jul 02 2016

a(n) ~ 40n log n. - Charles R Greathouse IV, Jul 02 2016

cp's OEIS Frontend

A142199 Primes congruent to 2 mod 41.

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A142200 Primes congruent to 3 mod 41.

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A142201 Primes congruent to 4 mod 41.

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A049573 Primes p such that x^41 = 2 has a solution mod p.

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A142204 Primes congruent to 7 mod 41.

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A142205 Primes congruent to 8 mod 41.

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A142206 Primes congruent to 9 mod 41.

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Magma

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A142208 Primes congruent to 11 mod 41.

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