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 1-6 of 6 results.

A040159 Primes p such that x^5 = 2 has a solution mod p.

Original entry on oeis.org

2, 3, 5, 7, 13, 17, 19, 23, 29, 37, 43, 47, 53, 59, 67, 73, 79, 83, 89, 97, 103, 107, 109, 113, 127, 137, 139, 149, 151, 157, 163, 167, 173, 179, 193, 197, 199, 223, 227, 229, 233, 239, 241, 251, 257, 263, 269, 277, 283, 293, 307, 313, 317, 337, 347, 349, 353
Offset: 1

Views

Author

N. J. A. Sloane

Keywords

Links

Crossrefs

Cf. A001132, A040028, A040098, A040160.
Has same beginning as A042991 but is strictly different.
For primes p such that x^m == 2 mod p has a solution for m = 2,3,4,5,6,7,... see A038873, A040028, A040098, A040159, A040992, A042966, ...

Programs

  • Magma
    [p: p in PrimesUpTo(400) | exists{x: x in ResidueClassRing(p) | x^5 eq 2}]; // Bruno Berselli, Sep 12 2012
  • Mathematica
    ok [p_]:=Reduce[Mod[x^5- 2, p]== 0, x, Integers]=!= False; Select[Prime[Range[180]], ok] (* Vincenzo Librandi, Sep 12 2012 *)

A215358 Primes congruent to {0, 2, 3, 4} mod 11.

Original entry on oeis.org

2, 3, 11, 13, 37, 47, 59, 79, 101, 103, 113, 157, 167, 179, 191, 211, 223, 233, 257, 277, 311, 367, 389, 409, 421, 431, 433, 443, 487, 499, 509, 521, 541, 563, 587, 607, 619, 631, 641, 653, 673, 719, 739, 751, 761, 773, 827, 829, 839, 883, 937, 971, 983
Offset: 1

Views

Author

Vincenzo Librandi, Aug 09 2012

Keywords

Links

Crossrefs

Cf. A000040, A042991, A045325.

Programs

  • Magma
    [p: p in PrimesUpTo(1000) | p mod 11 in [0, 2, 3, 4]];
  • Mathematica
    Select[Prime[Range[400]],MemberQ[{0,2,3,4},Mod[#,11]]&]

A215359 Primes congruent to {0, 2, 3, 4} mod 13.

Original entry on oeis.org

2, 3, 13, 17, 29, 41, 43, 67, 107, 173, 197, 199, 211, 223, 251, 263, 277, 353, 367, 379, 419, 431, 433, 457, 509, 523, 563, 587, 601, 613, 641, 653, 691, 719, 743, 757, 769, 797, 809, 821, 823, 887, 953, 977, 991, 1031, 1069, 1109, 1187, 1213, 1237
Offset: 1

Views

Author

Vincenzo Librandi, Aug 09 2012

Keywords

Comments

Apart from the 13 the same as A215280. - R. J. Mathar, Nov 26 2014

Links

Crossrefs

Cf. A000040, A042991, A045325.

Programs

  • Magma
    [p: p in PrimesUpTo(1500) | p mod 13 in [0, 2, 3, 4]];
  • Mathematica
    Select[Prime[Range[400]],MemberQ[{0,2,3,4},Mod[#,13]]&]

A215360 Primes congruent to {0, 2, 3, 4} mod 17.

Original entry on oeis.org

2, 3, 17, 19, 37, 53, 71, 89, 139, 157, 173, 191, 223, 241, 257, 293, 359, 461, 463, 479, 547, 563, 599, 631, 683, 701, 733, 751, 769, 853, 887, 937, 971, 1039, 1091, 1109, 1193, 1277, 1279, 1381, 1447, 1481, 1483, 1499, 1549, 1567, 1583, 1601
Offset: 1

Views

Author

Vincenzo Librandi, Aug 09 2012

Keywords

Links

Crossrefs

Cf. A000040, A042991, A045325.

Programs

  • Magma
    [p: p in PrimesUpTo(2000) | p mod 17 in [0, 2, 3, 4]];
  • Mathematica
    Select[Prime[Range[400]],MemberQ[{0,2,3,4},Mod[#,17]]&]

A215361 Primes congruent to {0, 2, 3, 4} mod 19.

Original entry on oeis.org

2, 3, 19, 23, 41, 59, 61, 79, 97, 137, 173, 193, 211, 251, 269, 307, 383, 401, 421, 439, 479, 593, 631, 743, 821, 839, 857, 859, 877, 953, 971, 991, 1009, 1049, 1087, 1123, 1163, 1181, 1201, 1237, 1277, 1409, 1427, 1429, 1447, 1523, 1543, 1579, 1619
Offset: 1

Views

Author

Vincenzo Librandi, Aug 09 2012

Keywords

Links

Crossrefs

Cf. A000040, A042991, A045325.

Programs

  • Magma
    [p: p in PrimesUpTo(2000) | p mod 19 in [0, 2, 3, 4]];
  • Mathematica
    Select[Prime[Range[400]],MemberQ[{0,2,3,4},Mod[#,19]]&]

A268063 Primes of the form (k^3 - k^2 - k - 1)/2 for some integer k > 0.

Original entry on oeis.org

7, 47, 599, 1567, 5807, 7487, 9463, 20807, 24623, 28879, 33599, 81647, 111599, 123007, 161839, 225263, 262399, 282407, 397807, 541007, 573247, 606743, 641519, 922807, 1115399, 1513727, 1577383, 1709999, 1779007, 1849847, 1997119, 2399039, 2573807, 2948399
Offset: 1

Views

Author

Emre APARI, Jan 25 2016

Keywords

Comments

Also primes of the form 4*k^3 + 4*k^2 - 1.

Examples

			k=15: (15^3 - 15^2 - 15 - 1)/2 = 1567 (is prime).

Links

Crossrefs

Cf. A004771, A042991, A168489.

Programs

  • Magma
    [a: n in [0..200] | IsPrime(a) where a is (n^3-n^2-n-1) div 2 ]; // Vincenzo Librandi, Jan 26 2016
  • Mathematica
    Select[Table[(n^3 - n^2 - n - 1) / 2, {n, 200}], PrimeQ] (* Vincenzo Librandi, Jan 26 2016 *)
  • PARI
    lista(nn) = for(n=1, nn, if(ispseudoprime(p=4*n^3+4*n^2-1), print1(p, ", "))); \\ Altug Alkan, Mar 14 2016
  • Sage
    [(k^3-k^2-k-1)/2 for k in [2*i+1 for i in [1..100]] if is_prime(Integer((k^3-k^2-k-1)/2))] # Tom Edgar, Jan 25 2016

Extensions

More terms from Tom Edgar, Jan 25 2016
Showing 1-6 of 6 results.

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

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