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 1-8 of 8 results.

A154834 Primes p such that p^5 - 2 is also prime.

Original entry on oeis.org

3, 13, 31, 139, 181, 211, 229, 271, 523, 619, 751, 853, 1063, 1483, 1699, 2791, 3361, 3463, 3541, 3769, 4051, 4201, 4801, 4861, 4903, 5521, 5689, 5701, 6163, 6211, 6763, 6823, 6949, 7621, 8059, 8269, 8389, 8419, 8563, 8689, 8713, 9001, 9103, 9319, 10303
Offset: 1

Views

Author

Vladimir Joseph Stephan Orlovsky, Jan 15 2009

Keywords

Comments

Primes in A154833.

Examples

			3^5 - 2 = 241 is prime,
13^5 - 2 = 371291 is prime, ...

Links

Crossrefs

Cf. A028870, A038599, A154831, A154832, A154833.

Programs

  • Mathematica
    lst={};Do[p=n^5-2;If[PrimeQ[p],If[PrimeQ[n],AppendTo[lst,n]]],{n,0,7!}];lst
Select[Prime[Range[1300]],PrimeQ[#^5-2]&] (* Harvey P. Dale, Feb 09 2019 *)

A154933 Numbers k such that k^6 - 2 is prime.

Original entry on oeis.org

3, 11, 17, 35, 37, 47, 49, 59, 67, 77, 99, 123, 127, 133, 139, 155, 161, 169, 173, 187, 195, 213, 225, 231, 237, 241, 245, 247, 253, 275, 279, 297, 319, 325, 367, 373, 381, 383, 385, 399, 411, 425, 431, 469, 507, 511, 523, 541, 545, 553, 569, 585, 589, 609
Offset: 1

Views

Author

Vladimir Joseph Stephan Orlovsky, Jan 17 2009

Keywords

Links

Crossrefs

Cf. A028870, A038599, A154831, A154832, A154833, A154834.

Programs

  • Mathematica
    lst={};Do[p=n^6-2;If[PrimeQ[p],AppendTo[lst,n]],{n,1,7!}];lst
  • PARI
    isA154933(n) = isprime(n^6-2) \\ Michael B. Porter, Oct 06 2009

Extensions

a(1) = 0 removed by Amiram Eldar, Apr 04 2020

A154935 Numbers n such that n^7-2 is prime.

Original entry on oeis.org

7, 15, 25, 87, 91, 99, 199, 211, 265, 337, 357, 361, 367, 405, 501, 511, 537, 595, 627, 685, 697, 771, 805, 841, 847, 861, 889, 931, 939, 979, 1035, 1047, 1081, 1125, 1135, 1177, 1225, 1231, 1287, 1315, 1321, 1387, 1425, 1497, 1501, 1627, 1741, 1795, 1807
Offset: 1

Views

Author

Vladimir Joseph Stephan Orlovsky, Jan 17 2009

Keywords

Links

Crossrefs

Cf. A028870, A038599, A154831, A154832, A154833, A154834, A154933, A154934.

Programs

  • Magma
    [n: n in [1..500]|IsPrime(n^7-2)]; // Vincenzo Librandi, Nov 26 2010
  • Mathematica
    lst={};Do[p=n^7-2;If[PrimeQ[p],AppendTo[lst,n]],{n,0,7!}];lst
Select[Range[2*10^3], PrimeQ[#^7 - 2] &] (* Vincenzo Librandi, Mar 20 2014 *)
  • PARI
    is(n)=isprime(n^7-2) \\ Charles R Greathouse IV, Feb 17 2017

A154934 Primes in A154933.

Original entry on oeis.org

3, 11, 17, 37, 47, 59, 67, 127, 139, 173, 241, 367, 373, 383, 431, 523, 541, 569, 613, 631, 673, 683, 691, 829, 967, 977, 1019, 1063, 1163, 1213, 1249, 1291, 1301, 1303, 1327, 1367, 1439, 1483, 1487, 1601, 1607, 1609, 1733, 1747, 1789, 1801, 1823, 1907
Offset: 1

Views

Author

Vladimir Joseph Stephan Orlovsky, Jan 17 2009

Keywords

Links

Crossrefs

Cf. A028870, A038599, A154831, A154832, A154833, A154834, A154933.

Programs

  • Mathematica
    lst={}; Do[p=n^6-2; If[PrimeQ[p], If[PrimeQ[n], AppendTo[lst,n]]], {n,0,3*7!}]; lst

A154936 Primes in A154935.

Original entry on oeis.org

7, 199, 211, 337, 367, 1231, 1321, 1627, 1741, 2161, 2251, 2551, 3259, 3769, 3877, 3931, 4099, 4591, 4759, 4789, 6829, 7297, 7867, 8221, 8887, 9049, 9181, 9337, 9349, 11959, 12697, 12919, 13411, 13591, 14827, 15187, 15217, 15817, 15877, 15889
Offset: 1

Views

Author

Vladimir Joseph Stephan Orlovsky, Jan 17 2009

Keywords

Links

Crossrefs

Cf. A028870, A038599, A154831, A154832, A154833, A154834, A154933, A154934, A154935.

Programs

  • Mathematica
    lst={}; Do[p=n^7-2; If[PrimeQ[p], If[PrimeQ[n], AppendTo[lst,n]]], {n,0,8!}]; lst

A071351 Numbers n such that both n^4 + 2 and n^4 - 2 are prime.

Original entry on oeis.org

3, 21, 87, 99, 129, 141, 279, 627, 657, 777, 783, 795, 1653, 1725, 1833, 1959, 2001, 2043, 3039, 3399, 3609, 3861, 3975, 4257, 4371, 4491, 5403, 5541, 5709, 5985, 7371, 7539, 7869, 7917, 8397, 8445, 8547, 8793, 9051, 9057, 9915, 9933, 11067, 12153
Offset: 1

Views

Author

Labos Elemer, May 21 2002

Keywords

Examples

			n=3: n^4 = 81; {79,83} are primes.

Links

Crossrefs

Cf. A028870, A038599, A154831, A154832, A154833, A154834, A154933, A154934, A154935, A154936. - Vladimir Joseph Stephan Orlovsky, Jan 17 2009

Programs

  • Mathematica
    lst={}; Do[p1=n^4-2; p2=n^4+2; If[PrimeQ[p1]&&PrimeQ[p2],AppendTo[lst,n]],{n,0,8!}]; lst (* Vladimir Joseph Stephan Orlovsky, Jan 17 2009 *)
Select[Range[730000], AllTrue[#^4 + {2, -2}, PrimeQ] &] (* The program uses the AllTrue function from Mathematica version 10 *) (* Harvey P. Dale, Jan 02 2018 *)

A154938 Numbers k such that k^6 - 2 and k^6 + 2 are both primes.

Original entry on oeis.org

195, 213, 231, 657, 1563, 1749, 2967, 3597, 3627, 4263, 4887, 6867, 6993, 7257, 7725, 9045, 9201, 9717, 11595, 12579, 13029, 14145, 14259, 14367, 15837, 16131, 16581, 17259, 19905, 19917, 21081, 21711, 23127, 24435, 24921, 28299, 28707
Offset: 1

Views

Author

Vladimir Joseph Stephan Orlovsky, Jan 17 2009

Keywords

Links

Crossrefs

Intersection of A154933 and A216978.
Cf. A028870, A038599, A154831, A154832, A154833, A154834, A154934, A154935, A154936, A071351.

Programs

  • Magma
    [n: n in [1..500] | IsPrime(n^6-2) and IsPrime(n^6+2)]; // Vincenzo Librandi, Nov 26 2010
  • Mathematica
    lst={};Do[p1=n^6-2;p2=n^6+2;If[PrimeQ[p1]&&PrimeQ[p2],AppendTo[lst,n]],{n,0,9!}];lst
Select[Range[30000],AllTrue[#^6+{2,-2},PrimeQ]&] (* Harvey P. Dale, Jun 21 2025 *)

A216945 Numbers k such that k-2, k^2-2, k^3-2, k^4-2 and k^5-2 are all prime.

Original entry on oeis.org

15331, 289311, 487899, 798385, 1685775, 1790991, 1885261, 1920619, 1967925, 2304805, 2479735, 3049201, 3114439, 3175039, 3692065, 4095531, 4653649, 5606349, 5708235, 6113745, 6143235, 6697425, 7028035, 7461601, 8671585, 8997121, 9260131, 10084915, 10239529
Offset: 1

Views

Author

Michel Lagneau, Sep 20 2012

Keywords

Comments

k^6-2 is also prime for k = 1685775, 4095531, 4653649, 5606349, 13219339, 13326069, 18439561, ...
Sequence is infinite under Schinzel's Hypothesis H. a(n) >> n log^5 n. - Charles R Greathouse IV, Sep 20 2012

Crossrefs

Cf. A052147, A028870, A038599, A154831, A154833, A154935.

Programs

  • Mathematica
    Select[Range[20000000], And@@PrimeQ/@(Table[n^i-2, {i, 1, 5}]/.n->#)&]
Select[Prime[Range[680000]]+2,AllTrue[#^Range[2,5]-2,PrimeQ]&] (* Requires Mathematica version 10 or later *) (* Harvey P. Dale, Sep 11 2020 *)

Formula

Sequence is A052147 intersection A028870 intersection A038599 intersection A154831 intersection A154833.
Showing 1-8 of 8 results.

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