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.

Previous Showing 11-15 of 15 results.

A227172 Numbers k such that (48^k + 47^k)/95 is prime.

Original entry on oeis.org

13, 31, 631, 5279, 36781
Offset: 1

Views

Author

Jean-Louis Charton, Jul 03 2013

Keywords

Comments

All terms are prime.
a(5) > 10^4.

Crossrefs

Programs

Extensions

a(5) from Michael S. Branicky, Jun 23 2025

A227173 Numbers k such that (138^k + 137^k)/275 is prime.

Original entry on oeis.org

7, 13, 2371, 2791, 2999, 4621, 8819, 21563
Offset: 1

Views

Author

Jean-Louis Charton, Jul 03 2013

Keywords

Comments

All terms are prime.

Crossrefs

Programs

Extensions

a(8) from Tyler Busby, Mar 19 2023

A227174 Numbers n such that (140^n + 139^n)/279 is prime.

Original entry on oeis.org

23, 41, 43, 151, 2927, 6133
Offset: 1

Views

Author

Jean-Louis Charton, Jul 03 2013

Keywords

Comments

All terms are prime.
a(7) > 10^4.
a(7) > 43400. - Lucas A. Brown, Nov 26 2020

Crossrefs

Programs

A301510 Smallest positive number b such that ((b+1)^prime(n) + b^prime(n))/(2*b + 1) is prime, or 0 if no such b exists.

Original entry on oeis.org

1, 1, 1, 1, 1, 1, 1, 1, 4, 1, 3, 16, 1, 11, 6, 37, 1, 9, 120, 9, 1, 2, 67, 16, 1, 26, 103, 12, 60, 1, 239, 4, 40, 2, 44, 174, 33, 1, 3, 260, 114, 1, 161, 70, 1, 3, 2, 3, 50, 45, 472, 228, 183, 66, 37, 7, 122, 235, 68, 102, 294, 8, 13, 1, 40, 62, 143, 1, 61, 7
Offset: 2

Views

Author

Tim Johannes Ohrtmann, Mar 22 2018

Keywords

Comments

Conjecture: a(n) > 0 for every n > 1.
Records: 1, 4, 16, 37, 120, 239, 260, 472, 917, 1539, 6633, 7050, 12818, ..., which occur at n = 2, 10, 13, 17, 20, 32, 41, 52, 72, 128, 171, 290, 309, ... - Robert G. Wilson v, Jun 16 2018

Examples

			a(10) = 4 because (5^29 + 4^29)/9 = 2149818248341 is prime and (2^29 + 1^29)/3, (3^29 + 2^29)/5 and (4^29 + 3^29)/7 are all composite.
		

Crossrefs

Numbers n such that ((b+1)^n + b^n)/(2*b + 1) is prime for b = 1 to 18: A000978, A057469, A128066, A128335, A128336, A187805, A181141, A187819, A217095, A185239, A213216, A225097, A224984, A221637, A227170, A228573, A227171, A225818.

Programs

  • Mathematica
    Table[p = Prime[n]; k = 1; While[q = ((b+1)^n+b^n)/(2*b+1); ! PrimeQ[q], k++]; k, {n, 200}]
    f[n_] := Block[{b = 1, p = Prime@ n}, While[! PrimeQ[((b +1)^p + b^p)/(2b +1)], b++]; b]; Array[f, 70, 2] (* Robert G. Wilson v, Jun 13 2018 *)
  • PARI
    for(n=2, 200, b=0; until(isprime((((b+1)^prime(n)+b^prime(n))/(2*b+1))), b++); print1(b,", ")) \\ corrected by Eric Chen, Jun 06 2018

Formula

a(n) = A250201(2*prime(n)) - 1 for n >= 2. - Eric Chen, Jun 06 2018

A301369 Numbers k such that (9^k + 7^k)/16 is prime.

Original entry on oeis.org

3, 107, 197, 2843, 3571, 4451, 31517, 44819
Offset: 1

Views

Author

Tim Johannes Ohrtmann, Mar 19 2018

Keywords

Comments

All terms are prime.
The corresponding primes are 67, 79401467172644850007356716446663549450843749853576087044440771380676673442288169290888310265443988907, ...

Crossrefs

Programs

  • Magma
    [n: n in [1..10000] |IsPrime((9^n+7^n)/16)]
  • Maple
    select(n->isprime((9^n+7^n)/16),[seq(n,n=1..10000,2)]); # Muniru A Asiru, Mar 27 2018
  • Mathematica
    Select[Range[1, 10000], PrimeQ[(9^n+7^n)/16] &]
  • PARI
    forprime(n=3, 10000, if(isprime((9^n+7^n)/16), print1(n, ", ")))
    

Extensions

a(7) from Michael S. Branicky, Apr 29 2023
a(8) from Michael S. Branicky, Jun 22 2024
Previous Showing 11-15 of 15 results.