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 15 results. Next

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

A213216 Numbers n such that (12^n + 11^n)/23 is prime.

Original entry on oeis.org

47, 401, 509, 8609
Offset: 1

Views

Author

Robert Price, Mar 02 2013

Keywords

Comments

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

Crossrefs

Programs

  • Mathematica
    Select[ Prime[ Range[1, 100000] ], PrimeQ[ (12^# + 11^#)/23 ]& ]
  • PARI
    is(n)=ispseudoprime((12^n+11^n)/23) \\ Charles R Greathouse IV, Feb 20 2017

Extensions

Removed incorrect first term of "2".

A221637 Numbers n such that (15^n + 14^n)/29 is prime.

Original entry on oeis.org

3, 127, 227, 1009, 1951, 5101, 14011
Offset: 1

Views

Author

Robert Price, May 28 2013

Keywords

Comments

All terms are prime.
a(8) > 10^5.

Crossrefs

Programs

  • Mathematica
    Select[ Prime[ Range[1, 100000] ], PrimeQ[ (15^# + 14^#)/29 ]& ]
  • PARI
    is(n)=ispseudoprime((15^n+14^n)/29) \\ Charles R Greathouse IV, Feb 20 2017

A185239 Numbers k such that (11^k + 10^k)/21 is prime.

Original entry on oeis.org

53, 421, 647, 1601, 35527
Offset: 1

Views

Author

Robert Price, Apr 05 2013

Keywords

Comments

All terms are prime.
a(6) > 10^5.

Crossrefs

Programs

  • Mathematica
    Select[ Prime[ Range[1, 100000] ], PrimeQ[ (11^# + 10^#)/21 ]& ]
  • PARI
    is(n)=ispseudoprime((11^n+10^n)/21) \\ Charles R Greathouse IV, May 22 2017

A227170 Numbers n such that (16^n + 15^n)/31 is prime.

Original entry on oeis.org

3, 5, 13, 1439, 1669, 37691
Offset: 1

Views

Author

Jean-Louis Charton, Jul 03 2013

Keywords

Comments

All terms are prime.
a(7) > 10^5. - Robert Price, Aug 26 2013

Crossrefs

Programs

A224501 Numbers n such that (11^n + 4^n)/15 is prime.

Original entry on oeis.org

7, 53, 67, 71, 443, 26497
Offset: 1

Views

Author

Robert Price, Apr 08 2013

Keywords

Comments

All terms are prime.
a(7) > 10^5.

Crossrefs

Programs

  • Mathematica
    Select[ Prime[ Range[1, 100000] ], PrimeQ[ (11^# + 4^#)/15 ]& ]
  • PARI
    is(n)=ispseudoprime((11^n+4^n)/15) \\ Charles R Greathouse IV, Jun 06 2017

A224984 Numbers n such that (14^n + 13^n)/27 is prime.

Original entry on oeis.org

7, 13, 311, 1637, 4363, 10433, 41669, 45631
Offset: 1

Views

Author

Robert Price, Apr 22 2013

Keywords

Comments

All terms are prime.
a(9) > 10^5.

Crossrefs

Programs

  • Mathematica
    Select[ Prime[ Range[1, 100000] ], PrimeQ[ (14^# + 13^#)/27 ]& ]
  • PARI
    forprime(p=3,10^6, if(ispseudoprime((14^p + 13^p)/27), print1(p,", ") ) ); \\ Joerg Arndt, Jul 29 2013

Extensions

Removed incorrect first term of "2".

A247244 Smallest prime p such that (n^p + (n+1)^p)/(2n+1) is prime, or -1 if no such p exists.

Original entry on oeis.org

3, 3, 3, 5, 3, 3, 7, 3, 7, 53, 47, 3, 7, 3, 3, 41, 3, 5, 11, 3, 3, 11, 11, 3, 5, 103, 3, 37, 17, 7, 13, 37, 3, 269, 17, 5, 17, 3, 5, 139, 3, 11, 78697, 5, 17, 3671, 13, 491, 5, 3, 31, 43, 7, 3, 7, 2633, 3, 7, 3, 5, 349, 3, 41, 31, 5, 3, 7, 127, 3, 19, 3, 11, 19, 101, 3, 5, 3, 3
Offset: 1

Views

Author

Eric Chen, Nov 28 2014

Keywords

Comments

All terms are odd primes.
a(79) > 10000, if it exists.
a(80)..a(93) = {3, 7, 13, 7, 19, 31, 13, 163, 797, 3, 3, 11, 13, 5}, a(95)..a(112) = {5, 2657, 19, 787, 3, 17, 3, 7, 11, 1009, 3, 61, 53, 2371, 5, 3, 3, 11}, a(114)..a(126) = {103, 461, 7, 3, 13, 3, 7, 5, 31, 41, 23, 41, 587}, a(128)..a(132) = {7, 13, 37, 3, 23}, a(n) is currently unknown for n = {79, 94, 113, 127, 133, ...} (see the status file under Links).

Examples

			a(10) = 53 because (10^p + 11^p)/21 is composite for all p < 53 and prime for p = 53.
		

Crossrefs

Programs

  • Mathematica
    lmt = 4200; f[n_] := Block[{p = 2}, While[p < lmt && !PrimeQ[((n + 1)^p + n^p)/(2n + 1)], p = NextPrime@ p]; If[p > lmt, 0, p]]; Do[Print[{n, f[n] // Timing}], {n, 1000}] (* Robert G. Wilson v, Dec 01 2014 *)
  • PARI
    a(n)=forprime(p=3, , if(ispseudoprime((n^p+(n+1)^p)/(2*n+1)), return(p)))

Formula

a(n) = 3 if and only if n^2 + n + 1 is a prime (A002384).

Extensions

a(43) from Aurelien Gibier, Nov 27 2023

A227171 Numbers n such that (18^n + 17^n)/35 is prime.

Original entry on oeis.org

3, 47, 53, 2411, 4057, 7963, 10273, 15737, 53299
Offset: 1

Views

Author

Jean-Louis Charton, Jul 03 2013

Keywords

Comments

All terms are prime.

Crossrefs

Programs

Extensions

a(7), a(8) from Richard Fischer, Aug 18 2013
a(9) from Robert Price, Aug 25 2013

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
Showing 1-10 of 15 results. Next