A040984 -id:A040984 - cp's OEIS frontend

A141908 Primes congruent to 2 mod 23.

2, 71, 163, 347, 439, 577, 761, 853, 991, 1129, 1451, 1543, 2003, 2141, 2371, 2417, 2647, 2693, 2969, 3061, 3613, 3659, 3797, 3889, 4027, 4073, 4211, 4349, 4441, 4993, 5039, 5407, 5591, 5683, 5821, 5867, 6143, 6373, 6833, 6971, 7109, 7247, 7477, 7523, 7753

Offset: 1

N. J. A. Sloane, Jul 11 2008

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

Cf. A000040, A040984.

[p: p in PrimesUpTo(8000) | p mod 23 eq 2 ]; // Vincenzo Librandi, Aug 16 2012

Select[Range[2,8000,23],PrimeQ] (* Vladimir Joseph Stephan Orlovsky, Apr 05 2011 *)

is(n)=isprime(n) && n%23==2 \\ Charles R Greathouse IV, Jul 01 2016

{2} UNION A142344. - R. J. Mathar, Jul 20 2008

A100201 Primes of the form 23n+3.

Original entry on oeis.org

3, 233, 463, 509, 601, 647, 739, 877, 1061, 1153, 1291, 1429, 1567, 1613, 1889, 2027, 2441, 2579, 2671, 3361, 3407, 3499, 3637, 3821, 4051, 4327, 4373, 4603, 4649, 4787, 5431, 5477, 5569, 6029, 6121, 6397, 6581, 6673, 6719, 6857, 6949, 7547, 7639, 7823

Offset: 1

Jun Mizuki (suzuki32(AT)sanken.osaka-u.ac.jp), Dec 27 2004

Vincenzo Librandi, Table of n, a(n) for n = 1..10000

Cf. A040984, A141908.

[ a: n in [0..400] | IsPrime(a) where a is 23*n+3 ]; // Vincenzo Librandi, Dec 07 2011

Select[Range[3,10000,23],PrimeQ] (* Vladimir Joseph Stephan Orlovsky, Apr 05 2011 *)

A212374 Primes congruent to 1 mod 23.

Original entry on oeis.org

47, 139, 277, 461, 599, 691, 829, 967, 1013, 1151, 1289, 1381, 1427, 1657, 1933, 1979, 2347, 2393, 2531, 3037, 3083, 3221, 3313, 3359, 3727, 3911, 4003, 4049, 4463, 4831, 4877, 4969, 5107, 5153, 5521, 5659, 5843, 5981, 6073, 6211, 6257, 6763, 6947, 7039, 7177

Offset: 1

Bruno Berselli, Sep 12 2012

This sequence is not the same as A040984. First disagreement at index 34: a(34)=5153, A040984(34)=5521.

Bruno Berselli, Table of n, a(n) for n = 1..1000

Cf. A100201, A102734, A141908-A141926, A040984.

[p: p in PrimesUpTo(7200) | p mod 23 eq 1];

select(p->irem(p, 23)=1, [ithprime(i)$i=1..1000])[]; # Alois P. Heinz, Sep 12 2012

Select[Prime[Range[1000]], Mod[#, 23] == 1 &]
Select[Range[1,7200,23],PrimeQ] (* Harvey P. Dale, Jul 02 2018 *)

is(n)=isprime(n) && n%23==1 \\ Charles R Greathouse IV, Jul 03 2016

a(n) ~ 22n log n. - Charles R Greathouse IV, Jul 03 2016

A049555 Primes p such that x^23 = 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, 53, 59, 61, 67, 71, 73, 79, 83, 89, 97, 101, 103, 107, 109, 113, 127, 131, 137, 149, 151, 157, 163, 167, 173, 179, 181, 191, 193, 197, 199, 211, 223, 227, 229, 233, 239, 241, 251, 257, 263, 269, 271, 281, 283

Offset: 1

N. J. A. Sloane

Complement of A040984 relative to A000040. - Vincenzo Librandi, Sep 14 2012

			0^23 == 2 (mod 2). 2^23 == 2 (mod 3). 3^23 == 2 (mod 5). 4^23 == 2 (mod 7). 7^23 == 2 (mod 11). 7^23 == 2 (mod 13). 9^23 == 2 (mod 17). 15^23 == 2 (mod 19). 2^23 == 2 (mod 23). 18^23 == 2 (mod 29). 4^23 == 2 (mod 31). 13^23 == 2 (mod 37). 5^23 == 2 (mod 41). 27^23 == 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, A040984.

[p: p in PrimesUpTo(300) | exists(t){x : x in ResidueClassRing(p) | x^23 eq 2}]; // Vincenzo Librandi, Sep 14 2012

ok[p_]:= Reduce[Mod[x^23 - 2, p] == 0, x, Integers] =!= False; Select[Prime[Range[150]], ok] (* Vincenzo Librandi, Sep 14 2012 *)

A102734 Primes of the form 23n+5.

Original entry on oeis.org

5, 97, 281, 373, 419, 557, 787, 971, 1063, 1109, 1201, 1523, 1753, 2029, 2213, 2351, 2719, 2857, 2903, 3041, 3271, 3547, 3593, 3823, 4007, 4099, 4283, 4421, 4513, 4651, 4789, 4973, 5387, 5479, 5801, 5939, 6353, 6491, 6997, 7043, 7411, 7457, 7549, 7687

Offset: 1

Jun Mizuki (suzuki32(AT)sanken.osaka-u.ac.jp), Feb 07 2005

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

Cf. A040984, A141908, A100201.

[a: n in [0..400]|IsPrime(a) where a is 23*n+5 ]; // Vincenzo Librandi, Jul 19 2012

Select[Range[5,10000,23],PrimeQ] (* Vladimir Joseph Stephan Orlovsky, Apr 05 2011 *)
Select[Table[23*n+5,{n,0,1500}],PrimeQ] (* Vincenzo Librandi, Jul 19 2012 *)

A141919 Primes congruent to 15 mod 23.

Original entry on oeis.org

61, 107, 199, 337, 383, 521, 613, 659, 751, 797, 1303, 1487, 1579, 1901, 1993, 2039, 2131, 2269, 2591, 2683, 2729, 3373, 3511, 3557, 3833, 4201, 4339, 4523, 4799, 4937, 5167, 5351, 5443, 5581, 5857, 5903, 6133, 6271, 6317, 6547, 6823, 6869, 6961, 7237, 7283

Offset: 1

N. J. A. Sloane, Jul 11 2008

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

Cf. A000040, A040984, A141908, A100201.

[p: p in PrimesUpTo(9000) | p mod 23 eq 15 ]; // Vincenzo Librandi, Aug 16 2012

Select[Range[15,10000,23],PrimeQ] (* Vladimir Joseph Stephan Orlovsky, Apr 05 2011 *)

is(n)=isprime(n) && n%23==15 \\ Charles R Greathouse IV, Jul 02 2016

a(n) ~ 22n log n. - Charles R Greathouse IV, Jul 02 2016

A141909 Primes congruent to 4 mod 23.

Original entry on oeis.org

73, 211, 257, 349, 487, 809, 947, 1039, 1223, 1361, 1453, 1499, 1637, 1867, 1913, 2143, 2281, 2557, 2741, 2833, 2879, 2971, 3109, 4259, 4397, 4673, 4903, 5087, 5179, 5501, 5639, 5869, 6007, 6053, 6329, 6421, 7019, 7433, 8123, 8353, 8537, 8629, 8951, 9043

Offset: 1

N. J. A. Sloane, Jul 11 2008

Primes congruent to 27 mod 46. - Chai Wah Wu, Apr 28 2025

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

Cf. A000040, A040984, A141908, A100201.

[p: p in PrimesUpTo(10000) | p mod 23 eq 4 ]; // Vincenzo Librandi, Aug 16 2012

Select[Range[4,10000,23],PrimeQ] (* Vladimir Joseph Stephan Orlovsky, Apr 05 2011 *)

is(n)=isprime(n) && n%23==4 \\ Charles R Greathouse IV, Jul 03 2016

a(n) ~ 22n log n. - Charles R Greathouse IV, Jul 03 2016

A141910 Primes congruent to 6 mod 23.

Original entry on oeis.org

29, 167, 397, 443, 673, 719, 811, 857, 1087, 1409, 1777, 1823, 2053, 2099, 2237, 2467, 2789, 2927, 3019, 3203, 3433, 3571, 3617, 3709, 3847, 4261, 4583, 4721, 4813, 4951, 5227, 5273, 5503, 5641, 5779, 6101, 6469, 6607, 6653, 6791, 6883, 7159, 7297, 7481

Offset: 1

N. J. A. Sloane, Jul 11 2008

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

Cf. A000040, A040984, A141908, A100201.

[p: p in PrimesUpTo(8000) | p mod 23 eq 6 ]; // Vincenzo Librandi, Aug 16 2012

Select[Range[6,10000,23],PrimeQ] (* Vladimir Joseph Stephan Orlovsky, Apr 05 2011 *)
Select[Prime[Range[1000]],Mod[#,23]==6&] (* Harvey P. Dale, Jun 20 2021 *)

is(n)=isprime(n) && n%23==6 \\ Charles R Greathouse IV, Jul 03 2016

a(n) ~ 22n log n. - Charles R Greathouse IV, Jul 03 2016

A141911 Primes congruent to 7 mod 23.

Original entry on oeis.org

7, 53, 191, 283, 421, 467, 743, 881, 1019, 1249, 1433, 1571, 1663, 1709, 1801, 1847, 2399, 2767, 3089, 3181, 3319, 3457, 3733, 3779, 3917, 4423, 4561, 5021, 5113, 5297, 5527, 5573, 5711, 5849, 5987, 6079, 6217, 6263, 6907, 7229, 7321, 7459, 7643, 7873, 7919

Offset: 1

N. J. A. Sloane, Jul 11 2008

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

Cf. A000040, A040984, A141908, A100201.

[p: p in PrimesUpTo(8000) | p mod 23 eq 7 ]; // Vincenzo Librandi, Aug 16 2012

Select[Range[7,10000,23],PrimeQ] (* Vladimir Joseph Stephan Orlovsky, Apr 05 2011 *)

is(n)=isprime(n) && n%23==7 \\ Charles R Greathouse IV, Jul 03 2016

a(n) ~ 22n log n. - Charles R Greathouse IV, Jul 03 2016

A141912 Primes congruent to 8 mod 23.

Original entry on oeis.org

31, 307, 353, 491, 859, 997, 1181, 1319, 1549, 1733, 1871, 2239, 2377, 2423, 2699, 2791, 2837, 3067, 3251, 3343, 3389, 3527, 3803, 4079, 4217, 4447, 4493, 4723, 4861, 4999, 5413, 5689, 5827, 6011, 6287, 6379, 6563, 6701, 6793, 6977, 7069, 7207, 7253, 7529

Offset: 1

N. J. A. Sloane, Jul 11 2008

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

Cf. A000040, A040984, A141908, A100201.

[p: p in PrimesUpTo(8000) | p mod 23 eq 8 ]; // Vincenzo Librandi, Aug 16 2012

Select[Range[8,10000,23],PrimeQ] (* Vladimir Joseph Stephan Orlovsky, Apr 05 2011 *)

is(n)=isprime(n) && n%23==8 \\ Charles R Greathouse IV, Jul 03 2016

a(n) ~ 22n log n. - Charles R Greathouse IV, Jul 03 2016

cp's OEIS Frontend

A141908 Primes congruent to 2 mod 23.

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A100201 Primes of the form 23n+3.

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A212374 Primes congruent to 1 mod 23.

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A049555 Primes p such that x^23 = 2 has a solution mod p.

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A102734 Primes of the form 23n+5.

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A141919 Primes congruent to 15 mod 23.

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Magma

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A141909 Primes congruent to 4 mod 23.

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Magma

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A141910 Primes congruent to 6 mod 23.

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