A102732 -id:A102732 - cp's OEIS frontend

A167119 Primes congruent to 2, 3, 5, 7 or 11 (mod 13).

2, 3, 5, 7, 11, 29, 31, 37, 41, 59, 67, 83, 89, 107, 109, 137, 163, 167, 193, 197, 211, 223, 239, 241, 263, 271, 293, 317, 349, 353, 367, 379, 397, 401, 419, 421, 431, 449, 457, 479, 499, 509, 523, 557, 577, 587, 601, 613, 631, 653, 661, 683, 691, 709, 733, 739, 743, 757

Offset: 1

Vladimir Joseph Stephan Orlovsky, Oct 27 2009

Primes which have a remainder mod 13 that is prime.

Union of A141858, A100202, A102732, A140371 and A140373. - R. J. Mathar, Oct 29 2009

			11 mod 13 = 11, 29 mod 13 = 3, 31 mod 13 = 5, hence 11, 29 and 31 are in the sequence.

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

Cf. A003627, A045326, A003631, A045309, A045314, A042987, A078403, A042993, A167134, A167135: primes p such that p mod k is prime, for k = 3..12 resp.

[ p: p in PrimesUpTo(740) | p mod 13 in {2, 3, 5, 7, 11} ]; // Klaus Brockhaus, Oct 28 2009

f[n_]:=PrimeQ[Mod[n,13]]; lst={};Do[p=Prime[n];If[f[p],AppendTo[lst,p]],{n,6,6!}];lst
Select[Prime[Range[4000]],MemberQ[{2, 3, 5, 7, 11},Mod[#,13]]&] (* Vincenzo Librandi, Aug 05 2012 *)

{forprime(p=2, 740, if(isprime(p%13), print1(p, ",")))} \\ Klaus Brockhaus, Oct 28 2009

Edited by Klaus Brockhaus and R. J. Mathar, Oct 28 2009 and Oct 29 2009

A140371 Primes of the form 26k + 7.

Original entry on oeis.org

7, 59, 137, 163, 241, 293, 397, 449, 631, 683, 709, 761, 787, 839, 1021, 1151, 1229, 1307, 1489, 1567, 1619, 1697, 1723, 1801, 1879, 1931, 2087, 2113, 2243, 2269, 2347, 2399, 2477, 2503, 2633, 2659, 2711, 2789, 2971, 3023, 3049, 3257, 3361, 3413, 3491, 3517

Offset: 1

Juri-Stepan Gerasimov, Jun 14 2008

nonn

Daniel Starodubtsev, Table of n, a(n) for n = 1..10000

Cf. A059245, A100202, A102732, A093191, A093350, A092178.

[a: n in [0..250]|IsPrime(a) where a is 26*n+7] // Vincenzo Librandi, Dec 18 2010

Select[Range[7, 30000, 26], PrimeQ] (* Vladimir Joseph Stephan Orlovsky, Jun 21 2011 *)

Edited by R. J. Mathar, Jun 16 2008

A140373 Primes of the form 26*n+11.

Original entry on oeis.org

11, 37, 89, 167, 193, 271, 349, 401, 479, 557, 661, 739, 947, 1051, 1103, 1129, 1181, 1259, 1493, 1571, 1597, 1753, 1831, 1987, 2039, 2143, 2221, 2273, 2351, 2377, 2663, 2689, 2741, 2767, 2819, 2897, 3001, 3079, 3209, 3313, 3391, 3469, 3547, 3677, 3833

Offset: 1

Juri-Stepan Gerasimov, Jun 14 2008

Also primes of the form 13*n+11. - N. J. A. Sloane, Jul 11 2008

Daniel Starodubtsev, Table of n, a(n) for n = 1..10000

Cf. A059245, A100202, A102732, A093191, A093350, A092178, A111369 (gives 2*n).

[a: n in [0..250]|IsPrime(a) where a is 26*n+11] // Vincenzo Librandi, Dec 18 2010

Select[Range[11, 50000, 13], PrimeQ] (* Vladimir Joseph Stephan Orlovsky, Jun 13 2011 *)

Edited by R. J. Mathar, Jun 16 2008

A140375 Primes of the form 26n+23.

Original entry on oeis.org

23, 101, 127, 179, 257, 283, 439, 491, 569, 647, 673, 751, 829, 881, 907, 1063, 1193, 1297, 1427, 1453, 1531, 1583, 1609, 1973, 1999, 2129, 2207, 2311, 2389, 2441, 2467, 2753, 2857, 2909, 3169, 3221, 3299, 3533, 3559, 3637, 3767, 3793, 3923, 4001, 4027

Offset: 1

Juri-Stepan Gerasimov, Jun 14 2008

Also primes congruent to 10 mod 13. - N. J. A. Sloane, Jul 11 2008

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

Cf. A000040, A059245, A100202, A102732, A093191, A093350, A092178.

[a: n in [0..250]|IsPrime(a) where a is 26*n+23]; // Vincenzo Librandi, Dec 18 2010

Select[Range[10, 50000, 13], PrimeQ] (* Vladimir Joseph Stephan Orlovsky, Jun 13 2011 *)
Select[Prime[Range[200]],MemberQ[{10},Mod[#,13]]&] (* Vincenzo Librandi, Aug 15 2012 *)

Edited by R. J. Mathar, Jun 16 2008

A154610 Numbers n such that 13n + 5 is prime.

Original entry on oeis.org

0, 2, 6, 8, 18, 24, 32, 38, 44, 56, 62, 66, 72, 74, 78, 84, 86, 92, 98, 108, 114, 128, 132, 134, 144, 162, 164, 174, 176, 182, 186, 198, 204, 206, 224, 228, 246, 248, 254, 258, 266, 272, 276, 282, 284, 296, 302, 318, 324, 326, 336, 342, 368, 378, 386, 392, 396

Offset: 1

Vincenzo Librandi, Jan 15 2009

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

Cf. A102732, A154609.

[n: n in [0..410] | IsPrime(13*n+5)]; // Vincenzo Librandi, Sep 24 2012

lst={};Do[p=13*n+5;If[PrimeQ[p],AppendTo[lst,n]],{n,0,6!}];lst (* Vladimir Joseph Stephan Orlovsky, Jul 01 2009 *)
Select[Range[0, 100], PrimeQ[13#+5]&] (* Vincenzo Librandi, Sep 24 2012 *)

is(n)=isprime(13*n+5) \\ Charles R Greathouse IV, Sep 24 2012

More terms from Vladimir Joseph Stephan Orlovsky, Jul 01 2009

A140372 Primes of the form 26k + 9.

Original entry on oeis.org

61, 113, 139, 191, 269, 347, 373, 503, 607, 659, 919, 971, 997, 1049, 1153, 1231, 1283, 1361, 1439, 1543, 1621, 1699, 1777, 1907, 1933, 2011, 2063, 2089, 2141, 2297, 2531, 2557, 2609, 2687, 2713, 2791, 2843, 2999, 3181, 3259, 3389, 3467, 3571, 3623, 3701

Offset: 1

Juri-Stepan Gerasimov, Jun 14 2008

Also primes of the form 13k + 9. - N. J. A. Sloane, Jul 11 2008

Harvey P. Dale, Table of n, a(n) for n = 1..1000

Cf. A059245, A100202, A102732, A093191, A093350, A092178.

[a: n in [0..250]|IsPrime(a) where a is 26*n+9] // Vincenzo Librandi, Dec 18 2010

Select[Range[9, 30000, 26], PrimeQ] (* Vladimir Joseph Stephan Orlovsky, Jun 21 2011 *)

Edited by R. J. Mathar, Jun 16 2008

A140374 Primes of the form 26k + 15.

Original entry on oeis.org

41, 67, 197, 223, 353, 379, 431, 457, 509, 587, 613, 691, 743, 769, 821, 977, 1237, 1289, 1367, 1471, 1523, 1549, 1601, 1627, 1783, 1861, 1913, 2017, 2069, 2251, 2381, 2459, 2693, 2719, 2797, 2927, 2953, 3083, 3109, 3187, 3343, 3499, 3733, 3863, 3889

Offset: 1

Juri-Stepan Gerasimov, Jun 14 2008

nonn

Cf. A059245, A100202, A102732, A093191, A093350, A092178.

[a: n in [0..250]|IsPrime(a) where a is 26*n+15] // Vincenzo Librandi, Dec 18 2010

Select[Range[15, 20000, 26], PrimeQ] (* Vladimir Joseph Stephan Orlovsky, Jun 18 2011 *)

Edited by R. J. Mathar, Jun 16 2008

A140376 Nonprimes of the form 26n+1.

Original entry on oeis.org

1, 27, 105, 183, 209, 235, 261, 287, 339, 365, 391, 417, 469, 495, 573, 625, 651, 703, 729, 755, 781, 807, 833, 885, 963, 989, 1015, 1041, 1067, 1119, 1145, 1197, 1275, 1353, 1379, 1405, 1431, 1457, 1509, 1535, 1561, 1587, 1639, 1665, 1691, 1717, 1743

Offset: 1

Juri-Stepan Gerasimov, Jun 14 2008

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

Cf. A059245, A100202, A102732, A093191, A093350, A092178.

[a: n in [0..80] | not IsPrime(a) where a is 26*n+1]; // Vincenzo Librandi, Mar 22 2014

Select[26 Range[0, 100] + 1, ! PrimeQ@# &] (* Vincenzo Librandi, Mar 22 2014 *)

Edited by R. J. Mathar, Jun 16 2008

A155935 Numbers n such that 13*n + 5 is not prime.

Original entry on oeis.org

1, 3, 4, 5, 7, 9, 10, 11, 12, 13, 14, 15, 16, 17, 19, 20, 21, 22, 23, 25, 26, 27, 28, 29, 30, 31, 33, 34, 35, 36, 37, 39, 40, 41, 42, 43, 45, 46, 47, 48, 49, 50, 51, 52, 53, 54, 55, 57, 58, 59, 60, 61, 63, 64, 65, 67, 68, 69, 70, 71, 73, 75, 76, 77, 79, 80, 81

Offset: 1

Vincenzo Librandi, Jan 31 2009

			Distribution of the even terms in the following triangular array::
*;
*,*;
*,*,*;
*,*,*,*;
*,*,*,*,*;
*,*,*,*,*,*;
*,*,*,10,*,*,*;
*,*,*,*,14,*,*,*;
4,*,*,*,*,*,*,*,*;
*,*,*,*,*,*,*,*,*,*;
*,*,12,*,*,*,*,*,*,*,*;
*,*,*,*,*,*,*,*,*,40,*,*; etc.
where * marks the non-integer values of (4*h*k + 2*k + 2*h - 4)/13 with h >= k >= 1. - _Vincenzo Librandi_, Jan 15 2013

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

Cf. A102732, A154610.

[n: n in [0..90] | not IsPrime(13*n + 5)];

Select[Range[0, 100], !PrimeQ[13 # + 5] &] (* Vincenzo Librandi, Oct 15 2012 *)

A274202 Primes congruent to 31 mod 65.

Original entry on oeis.org

31, 421, 811, 941, 1201, 1721, 2111, 2371, 3541, 3671, 3931, 4451, 5101, 5231, 5881, 6011, 6271, 6661, 6791, 8221, 8741, 9001, 9391, 9521, 9781, 10301, 10691, 11471, 11731, 12251, 12511, 12641, 13291, 13421, 13681, 14071, 14461, 14591, 14851, 15241, 15761

Offset: 1

Vincenzo Librandi, Jun 13 2016

Subsequence of A030430 and A102732.

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

Cf. A000040, A030430, A102732.

Cf. similar sequences of the type primes congruent to k mod 2*k+3: A045392 (k=2), A102732 (k=5), A138629 (k=7), A141873 (k=8), A141914 (k=10), A141935 (k=11), A141989 (k=13), A142018 (k=14), A142086 (k=16), A142126 (k=17), A142216 (k=19), A142269 (k=20), A142373 (k=22), A142433 (k=23), A142555 (k=25), A142619 (k=26), A142755 (k=28), A142827 (k=29), this sequence (k=31), A154621 (k=32), A154624 (k=34), A154628 (k=35).

[p: p in PrimesUpTo(20000) | p mod 65 eq 31];

Select[Prime[Range[2000]], MemberQ[{31}, Mod[#, 65]] &]
Select[Range[31,16000,65],PrimeQ] (* Harvey P. Dale, May 06 2018 *)

cp's OEIS Frontend

A167119 Primes congruent to 2, 3, 5, 7 or 11 (mod 13).

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A140371 Primes of the form 26k + 7.

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A140373 Primes of the form 26*n+11.

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A140375 Primes of the form 26n+23.

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A154610 Numbers n such that 13n + 5 is prime.

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A140372 Primes of the form 26k + 9.

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A140374 Primes of the form 26k + 15.

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A140376 Nonprimes of the form 26n+1.

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