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 1-4 of 4 results.

A050808 Numbers k such that floor(exp(k)) is prime.

Original entry on oeis.org

1, 2, 18, 50, 127, 141, 267, 310, 2290, 4487, 5391, 14025
Offset: 1

Views

Author

Patrick De Geest, Oct 15 1999

Keywords

Links

  • Eric Weisstein's World of Mathematics, e-Prime

Crossrefs

Cf. A050809 (the actual primes), A000149, A040016, A037028, A000227, A004791, A059791, A059792.

Programs

  • Mathematica
    Do[ If[ PrimeQ[ Floor[ \[ExponentialE]^n] ], Print[n] ], {n, 0, 4750} ]
Select[Range[15000],PrimeQ[Floor[Exp[#]]]&] (* Harvey P. Dale, Oct 16 2012 *)
  • PARI
    is(n)=ispseudoprime(exp(n)\1) \\ Charles R Greathouse IV, Jan 03 2014

Extensions

Corrected by Naohiro Nomoto, Feb 22 2001
More terms from Vladeta Jovovic, Feb 24 2001
More terms from Robert G. Wilson v, May 09 2001
a(11) = 5391 from Eric W. Weisstein, May 01 2006
a(12) from Donovan Johnson, Feb 04 2008

A059791 Numbers n such that floor(phi^n) is prime, where phi = golden ratio.

Original entry on oeis.org

2, 5, 6, 7, 11, 13, 17, 19, 24, 31, 37, 41, 47, 48, 53, 61, 71, 79, 96, 113, 313, 353, 503, 613, 617, 863, 1097, 1361, 4787, 4793, 5851, 7741, 8467, 10691, 12251, 13963, 14449, 19469, 35449, 36779, 44507, 51169, 56003, 81671, 89849, 94823, 140057, 148091, 159521, 183089, 193201, 202667
Offset: 1

Views

Author

Naohiro Nomoto, Feb 22 2001

Keywords

Comments

Tested up to n=250000. - Mark Rodenkirch, Feb 27 2020

Examples

			floor(phi^863)=227160876495918562748535035942584201965901433059749617\
427535706949917136103176482875403653972639455945062095866005032008819\
9236184776437699830957031191632116265394965429613743580479 is prime.

Links

  • Eric Weisstein's World of Mathematics, Phi-Prime

Crossrefs

Cf. A001622, A059792.

Programs

  • Mathematica
    Block[{$MaxExtraPrecision=10000}, Select[Range[14000],PrimeQ[ Floor[ GoldenRatio^#]]&]] (* Harvey P. Dale, Mar 06 2017 *)
  • PARI
    isok(n) = isprime(floor(((sqrt(5)+1)/2)^n)) \\ Michel Marcus, Jul 14 2013
Terms generated and tested with pfgw then verified with PARI using the following:
  • PARI
    c(n) = 3*fibonacci(n-1) + fibonacci(n-2) + (n % 2) - 1; ispseudoprime(c(n)) \\ Mark Rodenkirch, Feb 27 2020

Extensions

More terms from Vladeta Jovovic, Feb 24 2001
a(27)-a(33) from Eric W. Weisstein, May 01 2006
a(34)-a(36) from Dmitry Kamenetsky, Dec 29 2008
a(37)-a(52) from Mark Rodenkirch, Feb 27 2020

A077547 Primes of the form floor(Pi^k).

Original entry on oeis.org

3, 31, 97, 924269, 1958577254745770740635072198655932631
Offset: 1

Views

Author

Amarnath Murthy, Nov 09 2002

Keywords

Comments

The main entry for this sequence is A059792.
a(6) has 158 digits and is too large to include.

Links

  • Eric Weisstein's World of Mathematics, Pi-Prime

Crossrefs

Cf. A059792.

Programs

Extensions

a(5) from Vladimir Joseph Stephan Orlovsky, Jan 28 2009

A117839 Primes of the form floor(Pi^k + e^k).

Original entry on oeis.org

2, 5, 17, 9255121991, 28870447577
Offset: 1

Views

Author

Jonathan Vos Post, Apr 30 2006

Keywords

Comments

Intersection of A000040 and A061675.
The next term has 1535 digits. - Harvey P. Dale, Apr 26 2011

Crossrefs

See also A059792 (Numbers k such that floor(Pi^k) is prime) and their corresponding primes A077547.
See also A059303 (Numbers k such that floor(e^k) + 1 is prime) and their corresponding primes A118840.
Cf. A000040, A059303, A059792, A061675, A077547, A074496.

Programs

  • Mathematica
    Select[Table[Floor[\[Pi]^n+E^n],{n,0,5000}],PrimeQ]  (* Harvey P. Dale, Apr 26 2011 *)
Showing 1-4 of 4 results.

Started in 1964 by Neil J. A. Sloane | Maintained by The OEIS Foundation Inc.

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