A045319 -id:A045319

A045344

Primes congruent to {1, 2} mod 3.

+10
24

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

(list; graph; refs; listen; history; text; internal format)

OFFSET

1,1

COMMENTS

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

LINKS

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

FORMULA

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

MATHEMATICA

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 *)

PROG

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

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

CROSSREFS

Cf. A000040, A045372, A045391.

KEYWORD

nonn,easy

AUTHOR

N. J. A. Sloane

STATUS

approved

A045337

Primes congruent to {1, 2, 3, 4} (mod 7).

+10
6

2, 3, 11, 17, 23, 29, 31, 37, 43, 53, 59, 67, 71, 73, 79, 101, 107, 109, 113, 127, 137, 149, 151, 157, 163, 179, 191, 193, 197, 199, 211, 227, 233, 239, 241, 263, 269, 277, 281, 283, 311, 317, 331, 337, 347, 353

(list; graph; refs; listen; history; text; internal format)

OFFSET

1,1

LINKS

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

MATHEMATICA

Select[Prime[Range[600]], MemberQ[{1, 2, 3, 4}, Mod[#, 7]]&] (* Vincenzo Librandi, Aug 08 2012 *)

PROG

(Magma) [p: p in PrimesUpTo(400) | p mod 7 in [1, 2, 3, 4]]; // Vincenzo Librandi, Aug 08 2012

CROSSREFS

Cf. A000040, A045319.

KEYWORD

nonn,easy

AUTHOR

N. J. A. Sloane

STATUS

approved

A215302

Primes congruent to {1, 2, 3, 4} mod 11.

+10
4

2, 3, 13, 23, 37, 47, 59, 67, 79, 89, 101, 103, 113, 157, 167, 179, 191, 199, 211, 223, 233, 257, 277, 311, 331, 353, 367, 389, 397, 409, 419, 421, 431, 433, 443, 463, 487, 499, 509, 521, 541, 563, 587, 607, 617, 619, 631, 641, 653, 661, 673, 683, 719, 727

(list; graph; refs; listen; history; text; internal format)

OFFSET

1,1

LINKS

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

MATHEMATICA

Select[Prime[Range[600]], MemberQ[{1, 2, 3, 4}, Mod[#, 11]]&]

PROG

(Magma) [p: p in PrimesUpTo(1000) | p mod 11 in [1..4]];

CROSSREFS

Cf. A000040, A045319, A045337, A215303-A215305.

KEYWORD

nonn,easy

AUTHOR

Vincenzo Librandi, Aug 08 2012

STATUS

approved

A215305

Primes congruent to {1, 2, 3, 4} mod 19.

+10
4

2, 3, 23, 41, 59, 61, 79, 97, 137, 173, 191, 193, 211, 229, 251, 269, 307, 383, 401, 419, 421, 439, 457, 479, 571, 593, 631, 647, 743, 761, 821, 839, 857, 859, 877, 953, 971, 991, 1009, 1049, 1087, 1103, 1123, 1163, 1181, 1201, 1217, 1237, 1277

(list; graph; refs; listen; history; text; internal format)

OFFSET

1,1

LINKS

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

MATHEMATICA

Select[Prime[Range[600]], MemberQ[{1, 2, 3, 4}, Mod[#, 19]]&]

PROG

(Magma) [p: p in PrimesUpTo(1500) | p mod 19 in [1..4]];

CROSSREFS

Cf. A000040, A045319, A045337, A215302-A215304.

KEYWORD

nonn,easy

AUTHOR

Vincenzo Librandi, Aug 08 2012

STATUS

approved

A215303

Primes congruent to {1, 2, 3, 4} mod 13.

+10
3

2, 3, 17, 29, 41, 43, 53, 67, 79, 107, 131, 157, 173, 197, 199, 211, 223, 251, 263, 277, 313, 353, 367, 379, 419, 431, 433, 443, 457, 509, 521, 523, 547, 563, 587, 599, 601, 613, 641, 653, 677, 691, 719, 743, 757, 769, 797, 809, 821, 823, 859, 887, 911

(list; graph; refs; listen; history; text; internal format)

OFFSET

1,1

LINKS

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

MATHEMATICA

Select[Prime[Range[600]], MemberQ[{1, 2, 3, 4}, Mod[#, 13]]&]

PROG

(Magma) [p: p in PrimesUpTo(1000) | p mod 13 in [1..4]];

CROSSREFS

Cf. A000040, A045319, A045337, A215302-A215305.

KEYWORD

nonn,easy

AUTHOR

Vincenzo Librandi, Aug 08 2012

STATUS

approved

A215304

Primes congruent to {1, 2, 3, 4} mod 17.

+10
2

2, 3, 19, 37, 53, 71, 89, 103, 137, 139, 157, 173, 191, 223, 239, 241, 257, 293, 307, 359, 409, 443, 461, 463, 479, 547, 563, 599, 613, 631, 647, 683, 701, 733, 751, 769, 853, 887, 919, 937, 953, 971, 1021, 1039, 1091, 1109, 1123, 1193, 1259, 1277

(list; graph; refs; listen; history; text; internal format)

OFFSET

1,1

LINKS

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

MATHEMATICA

Select[Prime[Range[600]], MemberQ[{1, 2, 3, 4}, Mod[#, 17]]&]

PROG

(Magma) [p: p in PrimesUpTo(1500) | p mod 17 in [1..4]];

CROSSREFS

Cf. A000040, A045319, A045337, A215302-A215305.

KEYWORD

nonn,easy

AUTHOR

Vincenzo Librandi, Aug 08 2012

STATUS

approved