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 10 results.

A058780 Numbers n such that n^2 * 2^n + 1 is prime.

Original entry on oeis.org

1, 2, 3, 4, 21, 30, 33, 57, 100, 142, 144, 150, 198, 225, 304, 513, 782, 858, 3638, 6076, 9297, 11037, 12135, 12876, 30180, 48470
Offset: 1

Views

Author

Robert G. Wilson v, Jan 02 2001

Keywords

Links

Crossrefs

Cf. A282400, A058781, A005849.

Programs

  • Mathematica
    Do[ If[ PrimeQ[ n^2*2^n + 1 ], Print[n] ], {n, 1, 5000} ]
  • PARI
    is(n)=ispseudoprime(n^2*2^n+1) \\ Charles R Greathouse IV, May 22 2017

Extensions

More terms from Herman Jamke (hermanjamke(AT)fastmail.fm), Jan 05 2008

A367037 Numbers k such that k^3*2^k - 1 is a prime.

Original entry on oeis.org

2, 8, 31, 79, 661, 769, 1904, 2527, 9032, 15895, 19171
Offset: 1

Views

Author

Juri-Stepan Gerasimov, Nov 02 2023

Keywords

Comments

If it exists, a(12) > 100000. - Hugo Pfoertner, Nov 03 2023

Crossrefs

Numbers k such that k^m*2^k - 1 is prime: A000043 (m = 0), A002234 (m = 1), A058781 (m = 2), this sequence (m = 3).

Programs

  • Magma
    [k: k in [1..700] | IsPrime(k^3*2^k-1)];
  • Mathematica
    Select[Range[3000], PrimeQ[#^3*2^# - 1] &] (* Amiram Eldar, Nov 04 2023 *)

Extensions

a(11) from Hugo Pfoertner, Nov 02 2023

A367102 Numbers k such that k^4*2^k - 1 is a prime.

Original entry on oeis.org

3, 29, 43, 83, 133, 209, 271, 329, 415, 727, 2437, 5673, 6879, 7813, 8125, 11931, 29433, 29491, 38397, 91141, 99459, 110935, 127247
Offset: 1

Views

Author

Juri-Stepan Gerasimov, Nov 04 2023

Keywords

Crossrefs

Numbers k such that k^m*2^k - 1 is prime: A000043 (m = 0), A002234 (m = 1), A058781 (m = 2), A367037 (m = 3), this sequence (m = 4).

Programs

  • Magma
    [k: k in [1..500] | IsPrime(k^4*2^k-1)];
  • Mathematica
    Select[Range[6000], PrimeQ[#^4*2^# - 1] &] (* Amiram Eldar, Nov 05 2023 *)

Extensions

a(17)-a(18) from Amiram Eldar, Nov 05 2023
a(19) from Michael S. Branicky, Nov 05 2023
a(20)-a(23) from Hugo Pfoertner, Nov 08 2023, Nov 10 2023

A367464 Numbers k such that k^5*2^k - 1 is a prime.

Original entry on oeis.org

2, 6, 9, 18, 42, 132, 139, 482, 523, 524, 859, 909, 948, 979, 1158, 1741, 2364, 3519, 4388, 5952, 6266, 8564, 12169, 14448, 54944, 103526, 116563, 125918
Offset: 1

Views

Author

Juri-Stepan Gerasimov, Nov 18 2023

Keywords

Crossrefs

Numbers k such that k^m*2^k - 1 is a prime: A000043 (m = 0), A002234 (m = 1), A058781 (m = 2), A367037 (m = 3), A367102 (m = 4), this sequence (m = 5).
Cf. A367421.

Programs

  • Magma
    [k: k in [1..1000] | IsPrime(k^5*2^k-1)];
  • Mathematica
    Select[Range[2500], PrimeQ[#^5*2^# - 1] &] (* Amiram Eldar, Nov 19 2023 *)

Extensions

a(24)-a(25) from Michael S. Branicky, Nov 18 2023
a(26)-a(28) from Michael S. Branicky, Aug 26 2024

A367478 Numbers k such that k^6*2^k - 1 is a prime.

Original entry on oeis.org

37, 43, 167, 217, 239, 349, 581, 1297, 5183, 9119, 10589, 15205, 18745, 25687, 26609, 33667, 35663, 73603, 82501, 89269
Offset: 1

Views

Author

Juri-Stepan Gerasimov, Nov 19 2023

Keywords

Crossrefs

Numbers k such that k^m*2^k - 1 is a prime: A000043 (m = 0), A002234 (m = 1), A058781 (m = 2), A367037 (m = 3), A367102 (m = 4), A367464 (m = 5), this sequence (m = 6).

Programs

  • Magma
    [k: k in [1..1000] | IsPrime(k^6*2^k-1)];
  • Mathematica
    Select[Range[6000], PrimeQ[#^6*2^# - 1] &] (* Amiram Eldar, Nov 19 2023 *)

Extensions

a(12) inserted by and a(14)-a(17) from Michael S. Branicky, Nov 19 2023
a(18)-a(20) from Michael S. Branicky, Nov 21 2023

A279904 Primes of the form n^2*2^n - 1.

Original entry on oeis.org

71, 6271, 20971519999, 3696558092582911, 71248353479884799, 36607563614276605181951, 66626319770601443076406771711, 46716685589841799771959773105092594214371327, 3855174423960385883723562689229267550261846474751
Offset: 1

Views

Author

Juri-Stepan Gerasimov, Jan 17 2017

Keywords

Examples

			a(1) = 3^2*2^3 - 1 = 71 is prime where 3 = A058781(1).
a(2) = 7^2*2^7 - 1 = 6271 is prime where 7 = A058781(2).

Crossrefs

Cf. A058781.

Programs

  • Magma
    [a: n in [1..45] | IsPrime(a) where a is n^2*2^n-1];
  • Mathematica
    Select[Table[n^2 2^n - 1, {n, 0, 150}], PrimeQ] (* Vincenzo Librandi, Jan 20 2017 *)
  • PARI
    select(ispseudoprime, apply(n->n^2*2^n - 1, [1..200])) \\ Charles R Greathouse IV, Jan 20 2017

Formula

a(n) = A000040(A058781(n)).

A366956 Numbers k such that 3^k*k^3 - 2 is a prime.

Original entry on oeis.org

3, 15, 23, 53, 79, 1767, 2325, 2553, 8355, 12707, 13377, 17265, 30165, 45807, 65773, 98981
Offset: 1

Views

Author

Juri-Stepan Gerasimov, Oct 30 2023

Keywords

Crossrefs

Cf. A058780, A058781.

Programs

  • Magma
    [k: k in [1..500] | IsPrime(3^k*k^3-2)];
  • Mathematica
    Select[Range[3000], PrimeQ[3^#*#^3 - 2] &] (* Amiram Eldar, Oct 30 2023 *)

Extensions

a(10)-a(12) from Amiram Eldar, Oct 30 2023
a(13)-a(14) from Hugo Pfoertner, Oct 31 2023
a(15) from Michael S. Branicky, Nov 04 2023
a(16) from Michael S. Branicky, Aug 25 2024

A367561 Numbers k such that k^7*2^k - 1 is a prime.

Original entry on oeis.org

6, 45, 55, 80, 135, 187, 205, 384, 405, 1291, 1364, 2301, 2486, 2844, 16892, 27308, 30152, 32535, 45324, 71522, 72865
Offset: 1

Views

Author

Juri-Stepan Gerasimov, Nov 22 2023

Keywords

Comments

No further terms <= 100000. - Michael S. Branicky, Aug 28 2024

Crossrefs

Numbers k such that k^m*2^k - 1 is a prime: A000043 (m = 0), A002234 (m = 1), A058781 (m = 2), A367037 (m = 3), A367102 (m = 4), A367464 (m = 5), A367478 (m = 6), this sequence (m = 7).
Cf. A367560.

Programs

  • Magma
    [k: k in [1..4000] | IsPrime(k^7*2^k-1)];
  • Mathematica
    Select[Range[3000], PrimeQ[#^7*2^# - 1] &] (* Amiram Eldar, Nov 23 2023 *)

Extensions

a(16)-a(21) from Michael S. Branicky, Nov 23 2023

A237759 Numbers n such that either n^2*2^n-1 or n^2*2^n+1 is prime, but not both.

Original entry on oeis.org

1, 2, 4, 7, 21, 25, 30, 33, 41, 45, 57, 63, 83, 100, 131, 142, 144, 147, 150, 175, 198, 225, 304, 425, 449, 469, 513, 651, 782, 858, 1345, 1839, 1883, 1913, 2177, 2551, 2907, 3638, 3675, 6071, 6076, 9297, 11037, 11743, 12135, 12876, 14641, 38685, 40857
Offset: 1

Views

Author

Juri-Stepan Gerasimov, Feb 24 2014

Keywords

Examples

			4 is in the sequence because 4^2*2^4 - 1 = 16*16 - 1 = 255 is not a prime number but 4^2*2^4 + 1 = 16*16 + 1 = 257 is a prime number.

Crossrefs

Cf, A058781, A058780.

Programs

  • PARI
    isok(n) = isp1 = isprime(2^n*n^2-1); isp2 = isprime(2^n*n^2+1); (isp1 || isp2 && !(isp1 && isp2)); \\ Michel Marcus, Mar 05 2014

Extensions

Corrected by R. J. Mathar, Feb 26 2014

A367572 Numbers k such that k^8*2^k - 1 is a prime.

Original entry on oeis.org

5, 7, 49, 165, 251, 345, 385, 945, 949, 1001, 1963, 2113, 2249, 3751, 4381, 4911, 5133, 10039, 29693, 34901, 73885, 99319, 104883, 113613
Offset: 1

Views

Author

Juri-Stepan Gerasimov, Nov 23 2023

Keywords

Crossrefs

Numbers k such that k^m*2^k - 1 is a prime: A000043 (m = 0), A002234 (m = 1), A058781 (m = 2), A367037 (m = 3), A367102 (m = 4), A367464 (m = 5), A367478 (m = 6), A367561 (m = 7), this sequence (m = 8).

Programs

  • Magma
    [k: k in [1..4000] | IsPrime(k^8*2^k-1)];
  • Mathematica
    Select[Range[5000], PrimeQ[#^8*2^# - 1] &] (* Amiram Eldar, Nov 23 2023 *)

Extensions

a(19)-a(20) from Michael S. Branicky, Nov 23 2023
a(21) from Michael S. Branicky, Nov 25 2023
a(22)-a(24) from Michael S. Branicky, Aug 29 2024
Showing 1-10 of 10 results.

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

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