A142200 -id:A142200 - cp's OEIS frontend

A059236 Primes p such that x^41 = 2 has no solution mod p.

83, 739, 821, 1231, 1559, 1723, 2297, 2543, 2707, 2789, 2953, 3527, 3691, 4019, 5003, 5167, 5413, 5659, 5741, 5987, 6151, 6397, 6971, 7873, 8447, 8693, 9103, 9349, 9431, 9677, 9923, 10169, 10333, 11071, 11317, 11399, 12301, 12547, 13121, 13367

Offset: 1

Klaus Brockhaus, Jan 20 2001

Complement of A049573 relative to A000040.
Presumably this is also "Primes congruent to 1 mod 41" (A212379), but that requires a proof. - N. J. A. Sloane, Jul 11 2008
Smallest counterexample: 17467 is not in A059236, but congruent to 1 mod 41 (17467 = 426*41+1). - Klaus Brockhaus, May 18 2011

Klaus Brockhaus, Table of n, a(n) for n = 1..100000

Subsequence of A212379.

Cf. A049573, A142199, A142200, A190758.

[p: p in PrimesUpTo(13400) | not exists{x: x in ResidueClassRing(p) | x^41 eq 2}]; // Klaus Brockhaus, May 18 2011

/* Alternatively: */ [p: p in PrimesUpTo(13400) | forall{x: x in ResidueClassRing(p) | x^41 ne 2}]; // Bruno Berselli, Sep 20 2012

ok[p_]:= Reduce[Mod[x^41 - 2, p] == 0, x, Integers] == False; Select[Prime[Range[2000]], ok] (* Vincenzo Librandi, Sep 20 2012 *)
Select[Prime[Range[PrimePi[14000]]], ! MemberQ[PowerMod[Range[#], 41, #], Mod[2, #]] &] (* Bruno Berselli, Sep 20 2012 *)

forprime(p=2, 69589957, if(trap(, 1, sqrtn(Mod(2, p), 41); 0), print1(p,", "))) \\ Klaus Brockhaus, May 18 2011

N=10^5;  default(primelimit,N);
ok(p, r, k)={ return ( (p==r) || (Mod(r,p)^((p-1)/gcd(k,p-1))==1) ); }
forprime(p=2,N, if (! ok(p,2,41),print1(p,", ")));
/* Joerg Arndt, Sep 21 2012 */

A142199 Primes congruent to 2 mod 41.

Original entry on oeis.org

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

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

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

A142211 Primes congruent to 14 mod 41.

Original entry on oeis.org

137, 383, 547, 1039, 1367, 1531, 1613, 1777, 2269, 2351, 2843, 3089, 3253, 3499, 3581, 4073, 4483, 4729, 5303, 6287, 6451, 6779, 7517, 7681, 7927, 8009, 8419, 8501, 8747, 9157, 9239, 9403, 9649, 10141, 10223, 11617, 11699, 11863, 12109, 12437, 12601, 13093

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, A142210.

[p: p in PrimesUpTo(16000) | p mod 41 eq 14 ]; // Vincenzo Librandi, Aug 23 2012

Select[Range[14,30000,41],PrimeQ] (* Vladimir Joseph Stephan Orlovsky, May 17 2011 *)
Select[Prime[Range[5000]],MemberQ[{14},Mod[#,41]]&] (* Vincenzo Librandi, Aug 23 2012 *)

is(n)=isprime(n) && n%41==14 \\ Charles R Greathouse IV, Jul 02 2016

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

cp's OEIS Frontend

A059236 Primes p such that x^41 = 2 has no solution mod p.

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A142199 Primes congruent to 2 mod 41.

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A142201 Primes congruent to 4 mod 41.

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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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A142208 Primes congruent to 11 mod 41.

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A142209 Primes congruent to 12 mod 41.