cp's OEIS Frontend

This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.

Showing 1-10 of 11 results. Next

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

Original entry on oeis.org

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

Views

Author

Vladimir Joseph Stephan Orlovsky, Oct 27 2009

Keywords

Comments

Primes which have a remainder mod 13 that is prime.
Union of A141858, A100202, A102732, A140371 and A140373. - R. J. Mathar, Oct 29 2009

Examples

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

Links

Crossrefs

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.

Programs

  • Magma
    [ p: p in PrimesUpTo(740) | p mod 13 in {2, 3, 5, 7, 11} ]; // Klaus Brockhaus, Oct 28 2009
  • Mathematica
    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 *)
  • PARI
    {forprime(p=2, 740, if(isprime(p%13), print1(p, ",")))} \\ Klaus Brockhaus, Oct 28 2009

Extensions

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

Views

Author

Juri-Stepan Gerasimov, Jun 14 2008

Keywords

Links

Crossrefs

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

Programs

Extensions

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

Views

Author

Juri-Stepan Gerasimov, Jun 14 2008

Keywords

Comments

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

Links

Crossrefs

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

Programs

Extensions

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

Views

Author

Juri-Stepan Gerasimov, Jun 14 2008

Keywords

Comments

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

Links

Crossrefs

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

Programs

Extensions

Edited by R. J. Mathar, Jun 16 2008

A155853 Numbers n such that 13*n + 3 is a prime.

Original entry on oeis.org

0, 2, 8, 16, 20, 28, 32, 40, 46, 50, 58, 62, 68, 76, 82, 98, 100, 106, 110, 112, 116, 128, 130, 140, 146, 152, 160, 166, 170, 172, 188, 190, 196, 208, 218, 232, 250, 256, 266, 272, 278, 280, 296, 298, 302, 308, 316, 326, 338, 340, 358, 368, 370, 380, 382, 386
Offset: 1

Views

Author

Vincenzo Librandi, Jan 29 2009

Keywords

Comments

From Avik Roy (avik_3.1416(AT)yahoo.co.in), Feb 02 2009: (Start)
Only numbers of the form 6m+-2 can be included in this sequence.
All terms are evidently even and thus it can be concluded that 13n+3 can't be a prime if n itself is a prime greater than 2. (End)

Links

Crossrefs

Cf. A100202 (associated primes), A155854.

Programs

Extensions

More terms from Vladimir Joseph Stephan Orlovsky, Jul 01 2009

A155854 Numbers k such that 13*k + 3 is not prime.

Original entry on oeis.org

1, 3, 4, 5, 6, 7, 9, 10, 11, 12, 13, 14, 15, 17, 18, 19, 21, 22, 23, 24, 25, 26, 27, 29, 30, 31, 33, 34, 35, 36, 37, 38, 39, 41, 42, 43, 44, 45, 47, 48, 49, 51, 52, 53, 54, 55, 56, 57, 59, 60, 61, 63, 64, 65, 66, 67, 69, 70, 71, 72, 73, 74, 75, 77, 78, 79, 80, 81, 83, 84, 85, 86, 87
Offset: 1

Views

Author

Vincenzo Librandi, Jan 29 2009

Keywords

Links

Crossrefs

Cf. A100202, A155853.

Programs

  • Magma
    [n: n in [0..90] | not IsPrime(13*n + 3)]; // Vincenzo Librandi, Oct 15 2012
  • Mathematica
    Select[Range[100], !PrimeQ[13 # + 3] &]

Extensions

Data corrected by Harvey P. Dale, Sep 11 2011

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

Views

Author

Juri-Stepan Gerasimov, Jun 14 2008

Keywords

Comments

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

Links

Crossrefs

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

Programs

Extensions

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

Views

Author

Juri-Stepan Gerasimov, Jun 14 2008

Keywords

Crossrefs

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

Programs

Extensions

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

Views

Author

Juri-Stepan Gerasimov, Jun 14 2008

Keywords

Links

Crossrefs

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

Programs

  • Magma
    [a: n in [0..80] | not IsPrime(a) where a is 26*n+1]; // Vincenzo Librandi, Mar 22 2014
  • Mathematica
    Select[26 Range[0, 100] + 1, ! PrimeQ@# &] (* Vincenzo Librandi, Mar 22 2014 *)

Extensions

Edited by R. J. Mathar, Jun 16 2008

A322923 Primes of the form 3*p + 4, where p is a prime.

Original entry on oeis.org

13, 19, 37, 43, 61, 73, 97, 127, 163, 181, 223, 241, 271, 307, 313, 331, 397, 421, 457, 523, 541, 547, 577, 601, 673, 691, 727, 757, 811, 853, 883, 937, 997, 1051, 1063, 1123, 1153, 1171, 1231, 1297, 1303, 1321, 1531, 1567, 1627, 1693, 1783, 1801
Offset: 1

Views

Author

Vincenzo Librandi, Mar 12 2019

Keywords

Links

Crossrefs

Cf. A023209, A100202, A102851, A142120, A142262, A142817.

Programs

  • GAP
    P:=Filtered([1..1000],IsPrime);;
a:=Filtered(List(P,i->3*i+4),k->IsPrime(k)); # Muniru A Asiru, Mar 23 2019
  • Magma
    [a: p in PrimesUpTo(600) | IsPrime(a) where a is 3*p+4];
  • Maple
    select(isprime,[3*ithprime(p)+4$p=1..120]); # Muniru A Asiru, Mar 23 2019
  • Mathematica
    Select[Table[p=Prime[n];3p+4,{n,85}],PrimeQ]
  • PARI
    terms(n) = my(x=0, i=0); forprime(p=1, , if(i >= n, break); x=3*p+4; if(ispseudoprime(x), print1(x, ", "); i++))
/* Print initial 50 terms as follows: */
terms(50) \\ Felix Fröhlich, Mar 23 2019
Showing 1-10 of 11 results. Next

Started in 1964 by Neil J. A. Sloane | Maintained by The OEIS Foundation Inc.

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