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A074496 a(n) = smallest prime > e^n. 7
2, 3, 11, 23, 59, 149, 409, 1097, 2999, 8111, 22027, 59879, 162779, 442439, 1202609, 3269029, 8886113, 24154957, 65660003, 178482319, 485165237, 1318815761, 3584912873, 9744803489, 26489122147, 72004899361, 195729609461, 532048240609, 1446257064299, 3931334297161 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,1

COMMENTS

Where record values of floor(log(n/n’)) occur, where n’ is the arithmetic derivative of n. - Paolo P. Lava, Mar 20 2012

LINKS

Amiram Eldar, Table of n, a(n) for n = 0..2302

FORMULA

Lim_[n approaches infinity] a(n+1)/a(n) = e. - Jonathan Vos Post, Apr 30 2006

EXAMPLE

The first prime > e^3= 20.085.... is 23, so a(3) = 23.

MATHEMATICA

a[n_] := NextPrime[Exp[n]]; a /@ Range[0, 20] (* Giovanni Resta, Apr 03 2017 *)

PROG

(PARI) for(n=1, 50, print1(nextprime(exp(n))", "))

CROSSREFS

Cf. A000040, A000149, A014210, A014211, A074497.

Sequence in context: A246496 A119641 A252005 * A292817 A292112 A065849

Adjacent sequences:  A074493 A074494 A074495 * A074497 A074498 A074499

KEYWORD

nonn

AUTHOR

Joseph L. Pe, Sep 26 2002

EXTENSIONS

More terms from Ralf Stephan, Mar 25 2003

Edited by N. J. A. Sloane, Dec 22 2006

a(18) inserted and more terms added by Amiram Eldar, Sep 30 2019

STATUS

approved

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Last modified October 1 00:54 EDT 2020. Contains 337440 sequences. (Running on oeis4.)