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

A058781 Numbers k such that k^2 * 2^k - 1 is prime.

Original entry on oeis.org

3, 7, 25, 41, 45, 63, 83, 131, 147, 175, 425, 449, 469, 651, 1345, 1839, 1883, 1913, 2177, 2551, 2907, 3675, 6071, 11743, 14641, 38685, 40857, 47761, 97243
Offset: 1

Views

Author

Robert G. Wilson v, Jan 02 2001

Keywords

Comments

If it exists, a(30) > 200000. - Hugo Pfoertner, Nov 07 2023

Links

Crossrefs

Cf. A058780.

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

A357612 Numbers k such that 1 + 2^k*k^3 is prime.

Original entry on oeis.org

1, 5, 41, 202, 281, 394, 1157, 1211, 1816, 9845, 19780, 50800, 98621, 101945
Offset: 1

Views

Author

Juri-Stepan Gerasimov, Nov 17 2022

Keywords

Examples

			1 is in this sequence because 1 + 2^1*1^3 = 5 is prime;
5 is in this sequence because 1 + 2^5*5^3 = 4001 is prime.

Crossrefs

Cf. A000040, A005849, A058780.

Programs

  • Magma
    [n: n in [1..2000] | IsPrime(1+2^n*n^3)];
  • Mathematica
    Select[Range[2000], PrimeQ[1 + 2^# * #^3] &] (* Amiram Eldar, Nov 17 2022 *)

Extensions

a(11)-a(12) from Amiram Eldar, Nov 17 2022
a(13)-a(14) from Michael S. Branicky, May 16 2023

A366422 Numbers k such that k^4*2^k + 1 is a prime.

Original entry on oeis.org

1, 24, 33, 36, 99, 195, 244, 464, 567, 621, 741, 1395, 2164, 3309, 3537, 3708, 4413, 5001, 5187, 5292, 15504, 18816, 19521, 24657, 27972, 57687
Offset: 1

Views

Author

Juri-Stepan Gerasimov, Nov 16 2023

Keywords

Comments

No further terms <= 100000. - Michael S. Branicky, Nov 17 2023

Crossrefs

Numbers k such that k^m*2^k + 1 is a prime: 0, 1, 2, 4, 8, 16, .. (m = 0), A005849 (m = 1), A058780 (m = 2), A357612 (m = 3), this sequence (m = 4).
Cf. A092506, A367102.

Programs

  • Magma
    [k: k in [0..4000] | IsPrime(k^4*2^k+1)];
  • Mathematica
    Select[Range[6000], PrimeQ[#^4*2^# + 1] &] (* Amiram Eldar, Nov 16 2023 *)

Extensions

a(22)-a(25) from Amiram Eldar, Nov 17 2023
a(26) from Michael S. Branicky, Nov 17 2023

A367421 Numbers k such that k^5*2^k + 1 is a prime.

Original entry on oeis.org

1, 41, 53, 231, 532, 1632, 1642, 9701, 13372, 19613, 25518, 31929, 92476, 97433
Offset: 1

Views

Author

Juri-Stepan Gerasimov, Nov 18 2023

Keywords

Crossrefs

Numbers k such that k^m*2^k + 1 is a prime: 0, 1, 2, 4, 8, 16, .. (m = 0), A005849 (m = 1), A058780 (m = 2), A357612 (m = 3), A366422 (m = 4), this sequence (m = 5).

Programs

  • Magma
    [k: k in [1..1000] | IsPrime(k^5*2^k+1)];
  • Mathematica
    Select[Range[2000], PrimeQ[#^5*2^# + 1] &] (* Amiram Eldar, Nov 18 2023 *)

Extensions

a(10)-a(12) from Michael S. Branicky, Nov 18 2023
a(13)-a(14) from Michael S. Branicky, Aug 26 2024

A282400 Primes of the form n^2*2^n + 1.

Original entry on oeis.org

3, 17, 73, 257, 924844033, 966367641601, 9354438770689, 468230246058455728129, 12676506002282294014967032053760001, 112418056545792871256481555812420390351647277057, 462428252436731001462884654101636424188009906177, 32113073085884097323811434312613640568611799040001
Offset: 1

Views

Author

Abhiram R Devesh, Feb 19 2017

Keywords

Links

Crossrefs

Subset of A248917.
Cf. A058780 Numbers n such that n^2 * 2^n + 1 is prime.
Cf. A279904 Primes of the form n^2*2^n - 1.

Programs

  • Mathematica
    Select[Table[n^2 2^n+1,{n,200}],PrimeQ] (* Harvey P. Dale, Mar 26 2023 *)
  • Python
    import sympy
n = 1
while n < 100:
    q = (n**2) * (2**n) + 1
    if sympy.isprime(q):
        print(q)
    n += 1

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

A367287 Numbers k such that k^6*2^k + 1 is a prime.

Original entry on oeis.org

1, 2, 4, 62, 80, 122, 136, 658, 1918, 2998, 3404, 4042, 5678, 8378, 10438, 23530, 24610, 29090, 41650, 120818
Offset: 1

Views

Author

Juri-Stepan Gerasimov, Nov 21 2023

Keywords

Comments

No further terms <= 100000. - Michael S. Branicky, Nov 22 2023

Crossrefs

Numbers k such that k^m*2^k + 1 is a prime: 0, 1, 2, 4, 8, 16, .. (m = 0), A005849 (m = 1), A058780 (m = 2), A357612 (m = 3), A366422 (m = 4), A367421 (m = 5), this sequence (m = 6).
Cf. A367478.

Programs

  • Magma
    [k: k in [1..1000] | IsPrime(k^6*2^k + 1)];

Extensions

a(16)-a(19) from Michael S. Branicky, Nov 21 2023
a(20) from Michael S. Branicky, Aug 30 2024

A367560 Numbers k such that k^7*2^k + 1 is a prime.

Original entry on oeis.org

1, 3, 11, 51, 76, 123, 149, 274, 311, 328, 381, 639, 737, 898, 1156, 9017, 13200, 18348, 26388, 30081
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: 0, 1, 2, 4, 8, 16, .. (m = 0), A005849 (m = 1), A058780 (m = 2), A357612 (m = 3), A366422 (m = 4), A367421 (m = 5), A367287 (m = 6), this sequence (m = 7).
Cf. A092506.

Programs

  • Magma
    [k: k in [1..2000] | IsPrime(k^7*2^k+1)];

Extensions

a(18)-a(20) from Michael S. Branicky, Nov 22 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

A259298 Numbers k such that k^2*2^k + 3 is prime.

Original entry on oeis.org

0, 1, 2, 11, 22, 40, 79, 145, 152, 244, 271, 1471, 2516, 3460, 4130, 4550, 7534, 12973, 14051, 14176, 16093, 16952, 28565, 121319
Offset: 1

Views

Author

Juri-Stepan Gerasimov, Jun 23 2015

Keywords

Comments

Primes: 3, 5, 19, 247811, 2030043139, 1759218604441603,...

Examples

			2 is in this sequence because 2^2*2^2 + 3 = 19 and 19 is prime.

Crossrefs

Cf. A058780.

Programs

  • Magma
    [n: n in [0..1000] | IsPrime(n^2*2^n+3)];
  • Mathematica
    Select[Range[0, 10000], PrimeQ[#^2 2^# + 3] &] (* Vincenzo Librandi, Jun 25 2015 *)
  • PARI
    is(n)=ispseudoprime(n^2*2^n+3) \\ Charles R Greathouse IV, Jun 13 2017

Extensions

More terms from Vincenzo Librandi, Jun 25 2015
a(18)-a(22) from Jinyuan Wang, May 15 2020
a(23) from Michael S. Branicky, Apr 20 2023
a(24) from Michael S. Branicky, Jul 23 2024
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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