A045372 -id:A045372 - cp's OEIS frontend

A045344 Primes congruent to {1, 2} mod 3.

2, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47, 53, 59, 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, 233, 239, 241, 251, 257, 263, 269, 271, 277, 281, 283, 293, 307

Offset: 1

N. J. A. Sloane

Same as A045319, except for the 2nd term. - R. J. Mathar, Jan 30 2009
Primes of the form 3*n-+1. - Juri-Stepan Gerasimov, Jan 22 2010
Primes excluding 3. - Juri-Stepan Gerasimov, Apr 20 2010
Primes p such that p^2 + 2 is composite. 3 is the only prime p such that p^2 + 2 (= 11) is prime. All numbers p^2 + 2 for primes p = 2 and p > 3 are divisible by 3. - Jaroslav Krizek, Nov 25 2013
Primes p satisfying the equation gcd(sigma(p-1), p) = 1. - Lechoslaw Ratajczak, Aug 18 2018

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

Cf. A000040, A045372, A045391.

[p: p in PrimesUpTo(740)|p mod 3 in {1,2}] // Vincenzo Librandi, Dec 18 2010

Select[Prime[Range[150]], MemberQ[{1, 2}, Mod[#, 3]] &] (* Vladimir Joseph Stephan Orlovsky, Feb 18 2012 *)
Drop[Prime@ Range@ 63, {2}] (* Robert G. Wilson v, Jun 04 2015 *)

a(n)=if(n<2, 2, prime(n+1)) \\ Charles R Greathouse IV, May 13 2011

a(n) = A000040(A065475(n)). - Reinhard Zumkeller, Dec 17 2009

A045391 Primes congruent to {1, 2} mod 7.

Original entry on oeis.org

2, 23, 29, 37, 43, 71, 79, 107, 113, 127, 149, 163, 191, 197, 211, 233, 239, 281, 317, 331, 337, 359, 373, 379, 401, 421, 443, 449, 457, 463, 491, 499, 541, 547, 569, 617, 631, 653, 659, 673, 701, 709, 743, 751

Offset: 1

N. J. A. Sloane

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

Cf. A000040, A045344, A045372.

[p: p in PrimesUpTo(1000) | p mod 7 in [1, 2]]; // Vincenzo Librandi, Aug 10 2012

Select[Prime[Range[300]],MemberQ[{1,2},Mod[#,7]]&] (* Vincenzo Librandi, Aug 10 2012 *)
Select[Flatten[#+{1,2}&/@(7*Range[0,120])],PrimeQ] (* Harvey P. Dale, Sep 15 2019 *)

A215390 Primes congruent to {1, 2} mod 11.

Original entry on oeis.org

2, 13, 23, 67, 79, 89, 101, 167, 199, 211, 233, 277, 331, 353, 397, 409, 419, 431, 463, 541, 563, 607, 617, 661, 673, 683, 727, 739, 761, 827, 859, 881, 937, 947, 991, 1013, 1069, 1091, 1123, 1201, 1223, 1277, 1289, 1321, 1399, 1409, 1453, 1487

Offset: 1

Vincenzo Librandi, Aug 10 2012

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

Cf. A000040, A045344, A045372, A045391.

[p: p in PrimesUpTo(1500) | p mod 11 in [1, 2]];

Select[Prime[Range[300]],MemberQ[{1,2},Mod[#,11]]&]

A215391 Primes congruent to {1, 2} mod 13.

Original entry on oeis.org

2, 41, 53, 67, 79, 131, 157, 197, 223, 313, 353, 379, 431, 443, 457, 509, 521, 547, 587, 599, 613, 677, 691, 743, 769, 821, 859, 911, 937, 977, 1093, 1171, 1223, 1237, 1249, 1289, 1301, 1327, 1367, 1471, 1483, 1523, 1549, 1601, 1613, 1627, 1783, 1847

Offset: 1

Vincenzo Librandi, Aug 10 2012

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

Cf. A000040, A045344, A045372,

[p: p in PrimesUpTo(2000) | p mod 13 in [1, 2]];

Select[Prime[Range[300]],MemberQ[{1,2},Mod[#,13]]&]

A215392 Primes congruent to {1, 2} mod 17.

Original entry on oeis.org

2, 19, 53, 103, 137, 223, 239, 257, 307, 359, 409, 443, 461, 563, 613, 631, 647, 733, 919, 937, 953, 971, 1021, 1039, 1123, 1259, 1277, 1327, 1361, 1429, 1447, 1481, 1531, 1549, 1583, 1667, 1753, 1787, 1871, 1889, 1973, 2143, 2161, 2297, 2347, 2381, 2399, 2467

Offset: 1

Vincenzo Librandi, Aug 10 2012

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

Cf. A000040, A045344, A045372.

[p: p in PrimesUpTo(2500) | p mod 17 in [1, 2]];

Select[Prime[Range[300]],MemberQ[{1,2},Mod[#,17]]&]

A215393 Primes congruent to {1, 2} mod 19.

Original entry on oeis.org

2, 59, 97, 173, 191, 211, 229, 401, 419, 439, 457, 571, 647, 743, 761, 857, 971, 1009, 1103, 1123, 1217, 1237, 1427, 1483, 1559, 1579, 1597, 1693, 1787, 1901, 1997, 2053, 2111, 2129, 2243, 2281, 2339, 2357, 2377, 2699, 2719, 2833, 2851, 2909, 2927

Offset: 1

Vincenzo Librandi, Aug 10 2012

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

Cf. A000040, A045344, A045372.

[p: p in PrimesUpTo(3000) | p mod 19 in [1, 2]];

Select[Prime[Range[400]],MemberQ[{1,2},Mod[#,19]]&]

A290530 Primes congruent to (11,17) mod 30.

Original entry on oeis.org

11, 17, 41, 47, 71, 101, 107, 131, 137, 167, 191, 197, 227, 251, 257, 281, 311, 317, 347, 401, 431, 461, 467, 491, 521, 557, 587, 617, 641, 647, 677, 701, 761, 797, 821, 827, 857, 881, 887, 911, 941, 947, 971, 977, 1031, 1061, 1091, 1097, 1151, 1181, 1187, 1217, 1277

Offset: 1

Vincenzo Librandi, Aug 05 2017

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

Cf. A045372, A187058 (a subsequence).

[p: p in PrimesUpTo(1500) | p mod 30 in [11,17]];

Select[Prime@Range[210], MemberQ[{11, 17}, Mod[#, 30]] &]

cp's OEIS Frontend

A045344 Primes congruent to {1, 2} mod 3.

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A045391 Primes congruent to {1, 2} mod 7.

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A215390 Primes congruent to {1, 2} mod 11.

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A215391 Primes congruent to {1, 2} mod 13.

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A215392 Primes congruent to {1, 2} mod 17.

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A215393 Primes congruent to {1, 2} mod 19.

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A290530 Primes congruent to (11,17) mod 30.

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Mathematica