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 1-3 of 3 results.

A059792 Numbers k such that floor(Pi^k) is prime.

Original entry on oeis.org

1, 3, 4, 12, 73, 317, 2728, 6826, 7683, 7950, 14417, 44436, 63698
Offset: 1

Views

Author

Naohiro Nomoto, Feb 22 2001

Keywords

Examples

			Pi^3 = 31.0062766...; floor(Pi^3) = 31 is prime, hence 3 is a term.
		

Crossrefs

Programs

  • Mathematica
    Do[ If[ PrimeQ[ Floor[ Pi^n ] ], Print[n] ], {n, 0, 4000} ]
    $MaxExtraPrecision = 10^6; Do[k = Floor[Pi^n]; If[PrimeQ[k], Print[n]], {n, 1, 15000}] (* Ryan Propper, Oct 21 2005 *)

Extensions

More terms from Vladeta Jovovic, Feb 24 2001
One more term from Robert G. Wilson v, May 09 2001
a(8)-a(11) from Ryan Propper, Oct 21 2005
a(12)-a(13) from Donovan Johnson, Feb 05 2008

A109615 Primes of the form floor((Pi/2)^k).

Original entry on oeis.org

2, 3, 23, 37, 1373, 3389, 8363, 115459401415242179, 45851925215547567394556916118490828192232481476091362012033249370219, 1299908856087615767823951491725300134515972513464867209212961415385730635249
Offset: 1

Views

Author

Reinhard Zumkeller, Aug 01 2005

Keywords

Comments

The given terms of the sequence correspond to k=2, 3, 7, 8, 16, 18, 20 respectively. There are no other terms for k=21..100000. - Emeric Deutsch, Aug 27 2007

Examples

			A014214(20) = floor((Pi/2)^20) = floor(8363.6825...) = 8363 and 8363 = A000040(1047), therefore 8363 is a term.
		

Crossrefs

Intersection of A000040 and A014214.
Cf. A077547.

Programs

  • Maple
    a:=proc(n) if isprime(floor(((1/2)*Pi)^n))=true then floor(((1/2)*Pi)^n) else end if end proc: seq(a(n),n=1..100); # Emeric Deutsch, Aug 27 2007
  • Mathematica
    lst={};Do[If[PrimeQ[p=Floor[(Pi/2)^n]],AppendTo[lst,p]],{n,600}];lst

Extensions

a(8)-a(10) from Vincenzo Librandi, Dec 09 2011

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.

Programs

  • Mathematica
    Select[Table[Floor[\[Pi]^n+E^n],{n,0,5000}],PrimeQ]  (* Harvey P. Dale, Apr 26 2011 *)
Showing 1-3 of 3 results.