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.

A100408 Numbers n such that n^n-2 is prime.

Original entry on oeis.org

2, 7, 19, 21, 25, 49, 51, 1071
Offset: 1

Views

Author

Farideh Firoozbakht, Nov 19 2004

Keywords

Comments

Except for the first term all terms are odd.
Numbers n such that n^n+7 is prime gives the (as yet) too-short sequence 2,4,6,32,...
If it exists, a(9) > 25000. - Robert Price, Apr 25 2019

Examples

			51 is in the sequence because 51^51-2 is prime. 1071^1071-2 is a probable prime.

Crossrefs

Cf. A100407.

Programs

  • Mathematica
    Do[If[PrimeQ[n^n-2], Print[n]], {n, 1111}]
Select[Range[1111],PrimeQ[#^#-2]&] (* Harvey P. Dale, Dec 08 2024 *)
  • PARI
    is(n)=ispseudoprime(n^n-2) \\ Charles R Greathouse IV, Feb 20 2017

A166852 Numbers k such that k^k + 3 is prime.

Original entry on oeis.org

2, 1036, 2770
Offset: 1

Views

Author

Farideh Firoozbakht, Nov 20 2009

Keywords

Comments

Numbers corresponding to a(2) and a(3) are probable primes. 2770 is in the sequence so 2770^2770 + 3 is a probable prime; it is interesting that 277027703 is also prime. For the first term we have the same property: both 2^2 + 3 and 223 are prime.
For k = -1, k^k + 3 = 2 is prime but sequence focuses on the positive values of k. - Altug Alkan, Nov 28 2015
a(4) > 25000. - Michael S. Branicky, Oct 15 2024

Crossrefs

Cf. A087037, A100407, A100408, A166853.

Programs

  • Mathematica
    Do[If[GCD[n,3]==1&&PrimeQ[n^n+3],Print[n]],{n,2,5362,2}]
  • PARI
    is(n)=ispseudoprime(n^n+3) \\ Charles R Greathouse IV, Jun 13 2017

A166853 a(n) is the smallest number m such that m^m-n is prime, or zero if there is no such m.

Original entry on oeis.org

2, 2, 8, 3, 4, 5, 6, 3, 0, 3, 78, 13, 6, 3, 4, 3, 4, 17, 12, 3, 118, 3, 4, 3, 3
Offset: 1

Views

Author

Farideh Firoozbakht and M. F. Hasler, Nov 27 2009

Keywords

Comments

The sequence with the unknown terms a(n) indicated by -n:
(0's occur for n=9, 49, 81, 121....)
2,2,8,3,4,5,6,3,0,3,78,13,6,3,4,3,4,17,12,3,118,3,4,3,3,
-26,4,-28,4,487,90,9,4,-34,24,5,6,271,28,969,-41,5,-43,7,4,5,32,37,0,621,
20,15,34,7,6,9,4,5,4,7,-61,7,4,5,4,-66,6,63,134,27,10,35,102,31,4,
5,4,569,-79,13,0,15,4,5,-85,7,110,5,4,131,1122,7,4,11,8,7,6,9,4,-100,
22,5,-103,-104,4,5,4,11,12,39,-111,...
If they exist, the first two unknown terms, a(26) and a(28), they are greater than 10000. All other unknown terms a(n), for n<112 are greater than 4000.
If it exists, a(26) > 25000. - Robert Price, Apr 26 2019

Examples

			We have a(1)=2 since 1^1-1 is not prime, but 2^2-1 is prime.
a(9)=0 since 2^2-9 is not prime, and if m is an even number greater than 2 then m^m-9=(m^(m/2)-3)*(m^(m/2)+3) is composite. So there is no number m such that m^m-9 is prime. The same applies to any odd square > 25.
We have a(25)=3 since 3^3-25=2 is prime. But 25 is the only known square of the form m^m-2, so a(n)=0 for other odd squares > 25, e.g., n = 49,81,121,....
a(115)=2736 is the largest known term. 2736^2736-115 is a probable prime.

Crossrefs

Cf. A087037, A087038, A016754, A016923, A100407, A100408, A166852.

Formula

a(n)=0 if n=3^2 or n=(2k+1)^2 > 25, or n = (6k+1)^3 = A016923(k) with k>0.

A300292 Numbers k such that k^k + 9 is a prime.

Original entry on oeis.org

2, 130, 140
Offset: 1

Views

Author

Seiichi Manyama, Mar 16 2018

Keywords

Comments

No more terms <= 7000. - Jon E. Schoenfield, Mar 16 2018
No more terms <= 30000. - Michael S. Branicky, Sep 02 2024

Crossrefs

Numbers k such that k^k + b is a prime: A300981 (b=-10), A300976 (b=-5), A100408 (b=-2), A100407 (b=2), A166852 (b=3), A100837 (b=4), A100838 (b=7), this sequence (b=9), A100839 (b=10), A173974 (b=43).
Cf. A074966.

Programs

  • PARI
    isok(k) = ispseudoprime(k^k + 9); \\ Altug Alkan, Mar 16 2018

A300976 Numbers k such that k^k - 5 is a prime.

Original entry on oeis.org

4, 104, 124, 728
Offset: 1

Views

Author

Seiichi Manyama, Mar 17 2018

Keywords

Comments

728^728 - 5 is a probable prime.
Next term, if it exists, is greater than 5000. - Vaclav Kotesovec, Mar 25 2018
Next term, if it exists, is greater than 31000. - Robert Price, Mar 26 2018

Crossrefs

Numbers k such that k^k + b is a prime: A300981 (b=-10), this sequence (b=-5), A100408 (b=-2), A100407 (b=2), A166852 (b=3), A100837 (b=4), A100838 (b=7), A300292 (b=9), A100839 (b=10), A173974 (b=43).

Programs

  • Mathematica
    Select[Range[1000], PrimeQ[#^# - 5] &] (* Vaclav Kotesovec, Mar 25 2018 *)
  • PARI
    isok(k) = ispseudoprime(k^k - 5); \\ Altug Alkan, Mar 17 2018

A300981 Numbers k such that k^k - 10 is a prime.

Original entry on oeis.org

3, 9, 27, 249
Offset: 1

Views

Author

Seiichi Manyama, Mar 17 2018

Keywords

Comments

a(5), if it exists, is greater than 5000. - Vaclav Kotesovec, Mar 25 2018
a(5), if it exists, is greater than 25000. - Michael S. Branicky, Sep 02 2024

Crossrefs

Numbers k such that k^k + b is a prime: this sequence (b=-10), A300976 (b=-5), A100408 (b=-2), A100407 (b=2), A166852 (b=3), A100837 (b=4), A100838 (b=7), A300292 (b=9), A100839 (b=10), A173974 (b=43).

Programs

  • Mathematica
    Select[Range[1000], PrimeQ[#^# - 10] &] (* Vaclav Kotesovec, Mar 25 2018 *)
  • PARI
    isok(k) = ispseudoprime(k^k - 10); \\ Altug Alkan, Mar 17 2018
Showing 1-6 of 6 results.

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