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 1-7 of 7 results.

A187819 Numbers k such that (9^k + 8^k)/17 is prime.

Original entry on oeis.org

3, 7, 13, 19, 307, 619, 2089, 7297, 75571, 76103, 98897
Offset: 1

Views

Author

Robert Price, Dec 26 2012

Keywords

Comments

All terms are prime.
a(12) > 10^5.

Crossrefs

Programs

  • Mathematica
    Select[ Prime[ Range[1, 100000] ], PrimeQ[ (9^# + 8^#)/17 ]& ]
  • PARI
    is(n)=isprime((9^n+8^n)/17) \\ Charles R Greathouse IV, Feb 17 2017

A217095 Numbers n such that (10^n + 9^n)/19 is prime.

Original entry on oeis.org

7, 67, 73, 1091, 1483, 10937
Offset: 1

Views

Author

Robert Price, Feb 17 2013

Keywords

Comments

The numbers n themselves (7, 67, 73, ...) are also prime.
a(7) > 10^5.

Crossrefs

Programs

  • Mathematica
    Select[ Prime[ Range[1, 100000] ], PrimeQ[ (10^# + 9^#)/19 ]& ]
  • PARI
    is(n)=isprime((10^n+9^n)/19) \\ Charles R Greathouse IV, Feb 17 2017

A125958 Least number k > 0 such that (2^k + (2n-1)^k)/(2n+1) is prime.

Original entry on oeis.org

3, 3, 3, 5, 3, 3, 7, 3, 5, 5, 11, 3, 19, 11, 3, 229, 47, 5, 257, 3, 19, 31, 17, 11, 13, 3, 3, 5, 5, 59, 23, 3, 3, 7, 79, 3, 3373, 3, 3, 7, 13, 7, 7, 3527, 593, 19, 3, 3, 13, 13, 11, 19, 41, 3, 7, 109, 3, 227, 13, 5, 5, 3, 239, 5, 3251, 3, 1237, 3, 7, 31, 3, 7
Offset: 1

Views

Author

Alexander Adamchuk, Feb 06 2007

Keywords

Comments

All terms are odd primes.
a(38),...,a(43) = {3,3,7,13,7,7}.
a(46),...,a(64) = {19,3,3,13,13,11,19,41,3,7,109,11,227,13,5,5,3,239,5}.
a(66) = 3. a(68),...,a(72) = {3,7,31,3,7}.
a(74),...,a(92) = {3,5,19,17,3,83,3,3,19,19,11,11,61,3,7,7,3,41,29}.
a(94) = 5. a(97),a(98) = {19,7}. a(100) = 31.
a(n) is currently unknown for n = {37,44,45,65,67,73,93,95,96,99,...}.
From Kevin P. Thompson, May 18 2022: (Start)
All known terms from n=1..100 correspond to proven primes.
a(96) > 10250.
a(99) > 10250. (End)
Presuming every prime is seen at least once, one can specifically seek those with fixed k. Doing this, a(174) = 37, a(368) = 43 for example. - Bill McEachen, Aug 26 2024

Examples

			For n=4, the expression (2^k + (2n-1)^k)/(2n+1) takes on values 1, 53/9, 39, 2417/9, and 1871 for k=1..5. Since 1871 is the first prime number to occur, a(4) = 5.
		

Crossrefs

Cf. A000978 ((2^n + 1)/3 is prime), A057469 ((2^n + 3^n)/5 is prime).
Cf. A082387 ((2^n + 5^n)/7 is prime), A125955 ((2^n + 7^n)/9 is prime).
Cf. A125956 ((2^n + 9^n)/11 is prime), A125955 ((2^n + 11^n)/13 is prime).

Programs

  • Mathematica
    Do[k = 1; While[ !PrimeQ[(2^k + (2n-1)^k)/(2n+1)], k++ ]; Print[k], {n, 100}] (* Ryan Propper, Mar 29 2007 *)

Extensions

More terms from Ryan Propper, Mar 29 2007
a(65)-a(72) from Kevin P. Thompson, May 18 2022

A225191 Numbers n such that (15^n + 2^n)/17 is prime.

Original entry on oeis.org

3, 67, 199, 479, 563, 2243, 2579, 6599, 7951, 10099, 10909, 13759
Offset: 1

Views

Author

Robert Price, May 07 2013

Keywords

Comments

All terms are odd primes.
a(13) > 10^5.

Crossrefs

Programs

  • Mathematica
    Select[Prime[Range[1, 100000]], PrimeQ[(15^# + 2^#)/17]&]
  • PARI
    forprime(p=3,10^6, if(ispseudoprime((15^p + 2^p)/17), print1(p,", ") ) ); \\ Joerg Arndt, Jul 29 2013

Extensions

Removed incorrect first term of "2".

A222265 Numbers n such that (13^n + 2^n)/15 is prime.

Original entry on oeis.org

7, 31, 103, 223, 503, 1171, 1973, 4111, 4729
Offset: 1

Views

Author

Robert Price, May 05 2013

Keywords

Comments

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

Crossrefs

Programs

  • Mathematica
    Select[Prime[Range[1, 100000]], PrimeQ[(13^# + 2^#)/15]&]
  • PARI
    forprime(p=3,10^6, if(ispseudoprime((13^p + 2^p)/15), print1(p,", ") ) ); \\ Joerg Arndt, Jul 29 2013

Extensions

Removed incorrect first term of "2".

A211409 Numbers n such that (9^n + 4^n)/13 is prime.

Original entry on oeis.org

3, 5, 7, 11, 17, 19, 41, 53, 109, 167, 2207, 3623, 5059, 5471, 7949, 21211, 32993, 60251
Offset: 1

Views

Author

Robert Price, Feb 09 2013

Keywords

Comments

All terms are prime.
The next element, a(19), is greater than 10^5.

Crossrefs

Programs

  • Mathematica
    Select[ Prime[ Range[1, 100000] ], PrimeQ[ (9^# + 4^#)/13 ]& ]
  • PARI
    is(n)=ispseudoprime((9^n+4^n)/13) \\ Charles R Greathouse IV, Jun 13 2017

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
Showing 1-7 of 7 results.