A040016 -id:A040016 - cp's OEIS frontend

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

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

Offset: 1

Patrick De Geest, Oct 15 1999

Eric Weisstein's World of Mathematics, e-Prime

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

Do[ If[ PrimeQ[ Floor[ \[ExponentialE]^n] ], Print[n] ], {n, 0, 4750} ]
Select[Range[15000],PrimeQ[Floor[Exp[#]]]&] (* Harvey P. Dale, Oct 16 2012 *)

is(n)=ispseudoprime(exp(n)\1) \\ Charles R Greathouse IV, Jan 03 2014

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

Patrick De Geest, Oct 15 1999

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

Amiram Eldar, Table of n, a(n) for n = 1..9
Eric Weisstein's World of Mathematics, e-Prime.

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

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

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

Jeppe Stig Nielsen, Feb 14 2024

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.

			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.

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

default(realprecision,2000);for(k=1,+oo,r=exp(k);abs(r-(precprime(r)+nextprime(r))/2)<1&&print1(k,", "))

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

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

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Mathematica

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

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Examples

Crossrefs

Programs

PARI