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.

A126137 a(n) = pi(A037028(n)).

Original entry on oeis.org

1, 2, 4, 8, 16, 35, 79, 184, 429, 1019, 2467, 6049, 14912, 37128, 93117, 234855, 595341, 1516234, 3877186, 9950346, 25614563, 66124777, 171141897, 443963543, 1154106845, 3005936865, 7842921261, 20496470802, 53645077679, 140599114669, 368973074566, 969455391691
Offset: 0

Views

Author

Gary W. Adamson, Dec 18 2006

Keywords

Examples

			a(3) = 8 since A037028(3) = 19 and 19 = the 8th prime.
a(4) = 16 since A037028(4) = 53 and 53 = the 16th prime.

Links

Crossrefs

Cf. A000720, A037028.

Programs

  • Mathematica
    Table[np=NextPrime[E^n];pp=NextPrime[E^n,-1];If[E^n-ppJames C. McMahon, Dec 25 2024 *)

Extensions

Name edited by and more terms from Jinyuan Wang, Apr 10 2020
Offset corrected by James C. McMahon, Dec 25 2024

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

A050809 Primes of the form floor( exp(k) ).

Original entry on oeis.org

2, 7, 65659969, 5184705528587072464087, 14302079958348104463583671072905261080748384225250684971, 17199742630376622641833783925547830057256484050709158699244513
Offset: 1

Views

Author

Patrick De Geest, Oct 15 1999

Keywords

Examples

			a(3) = floor(e^18) = 65659969, which is prime.

Links

Crossrefs

Cf. A050808 (values of k), A000149, A040016, A037028, A000227, A004791.

Programs

  • Mathematica
    Select[Table[Floor[Exp[n]], {n, 150}], PrimeQ] (* Jayanta Basu, Jun 01 2013 *)

Extensions

Corrected by Naohiro Nomoto, Feb 22 2001

A370305 Numbers k such that the distance from exp(k) to the closest average of two consecutive primes is less than 1.

Original entry on oeis.org

1, 3, 16, 61, 74, 91, 113, 1441, 1566, 2170, 2499
Offset: 1

Views

Author

Jeppe Stig Nielsen, Feb 14 2024

Keywords

Comments

Explicitly, abs( e^k - (prevprime(e^k)+nextprime(e^k))/2 ) < 1.
For k>1, the formula (prevprime(e^k)+nextprime(e^k))/2 either gives floor(e^k), for k = 61, 74, 2170, ..., or gives ceiling(e^k), for k = 3, 16, 91, 113, 1441, 1566, 2499, ... This partitions {a(n)}\{1} into two subsequences each of which can be conjectured to have relative density 1/2.
In cases k = 16, 61, 113, 2499, ... the distance is actually less than 0.5. Then the formula (prevprime(e^k)+nextprime(e^k))/2 yields round(e^k), the nearest integer to e^k.

Examples

			For k=16, e^16 is about 8886110.52. The next prime is 8886113, and the previous prime is 8886109, and their average 8886111 is at a distance of about 0.48 away from e^16.

Crossrefs

Cf. A037028, A040016, A050808, A059303, A074496.

Programs

  • PARI
    default(realprecision,2000);for(k=1,+oo,r=exp(k);abs(r-(precprime(r)+nextprime(r))/2)<1&&print1(k,", "))
Showing 1-4 of 4 results.

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

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