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.

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

A242517 List of primes p for which p^n - 2 is prime for n = 1, 3, and 5.

Original entry on oeis.org

31, 619, 2791, 4801, 15331, 33829, 40129, 63421, 69151, 98731, 127291, 142789, 143569, 149971, 151849, 176599, 184969, 201829, 210601, 225289, 231841, 243589, 250951, 271279, 273271, 277549, 280591, 392269, 405439, 441799, 472711, 510709, 530599, 568441, 578689
Offset: 1

Views

Author

Abhiram R Devesh, May 17 2014

Keywords

Examples

			31 is in the sequence because
p = 31 (prime),
p - 2 = 29 (prime),
p^3 - 2 = 29789 (prime), and
p^5 - 2 = 28629149 (prime).

Links

Crossrefs

Intersection of A006512, A178251 and A154834, hence, intersection of A240126 and A154834.
Cf. A001359.

Programs

  • Mathematica
    Select[Range[600000], PrimeQ[#] && AllTrue[#^{1, 3, 5} - 2, PrimeQ] &] (* Amiram Eldar, Apr 06 2020 *)
  • PARI
    isok(p) = isprime(p) && isprime(p-2) && isprime(p^3-2) && isprime(p^5-2); \\ Michel Marcus, Apr 06 2020
  • PARI
    list(lim)=my(v=List(),p=29); forprime(q=31,lim, if(q-p==2 && isprime(q^3-2) && isprime(q^5-2), listput(v,q)); p=q); Vec(v) \\ Charles R Greathouse IV, Apr 06 2020
  • Python
    import sympy
n=2
while n>1:
    n1=n-2
    n2=((n**3)-2)
    n3=((n**5)-2)
    ##Check if n1, n2 and n3 are also primes.
    if sympy.ntheory.isprime(n1)== True and sympy.ntheory.isprime(n2)== True and sympy.ntheory.isprime(n3)== True:
        print(n, " , " , n1, " , ", n2, " , ", n3)
    n=sympy.ntheory.nextprime(n)

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 *)

A258572 Primes p such that p - 2, p^2 - 2, p^3 - 2, p^4 - 2 and p^5 - 2 are all prime.

Original entry on oeis.org

15331, 3049201, 9260131, 10239529, 10955449, 24303469, 33491569, 42699721, 56341711, 66241561, 87068479, 114254629, 129783571, 143927419, 152065549, 221977909, 235529419, 252769399, 280028449, 284535481, 299116021, 312896359, 349665889, 361039519, 407462929
Offset: 1

Views

Author

Juri-Stepan Gerasimov, Jun 03 2015

Keywords

Comments

Intersection of A006512, A062326, A178251, A154832 and A154834.
Subsequence of primes of A216945. - Michel Marcus, Jul 07 2015

Crossrefs

Cf. A006512, A062326, A154832, A154834, A178251, A216945.

Programs

  • Magma
    [p: p in PrimesUpTo(40000000) | IsPrime(p^1-2) and IsPrime(p^2-2) and IsPrime(p^3-2) and IsPrime(p^4-2) and IsPrime(p^5-2)];
  • Mathematica
    Select[Prime[Range[10^8]], And@@PrimeQ[{#, # - 2, #^2 - 2, #^3 - 2, #^4 - 2, #^5 - 2}] &] (* Vincenzo Librandi, Jul 06 2015 *)
Select[Prime[Range[2172*10^4]],AllTrue[#^Range[5]-2,PrimeQ]&] (* The program uses the AllTrue function from Mathematica version 10 *) (* Harvey P. Dale, Dec 02 2018 *)
  • PARI
    first(m)=my(v=vector(m),i,p,t=1);for(i=1,m,while(1,p=prime(t);if(isprime(p-2)&&isprime(p^2 - 2)&&isprime(p^3 - 2)&&isprime(p^4 - 2)&&isprime(p^5 - 2),v[i]=p;break,t++));t++);v; /* Anders Hellström, Jul 17 2015 */

Extensions

a(10) corrected and a(14)-a(25) added by Giovanni Resta, Jun 05 2015
Showing 1-8 of 8 results.

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

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