

A061273


Number of primes between successive powers of e (= 2.718281828...).


3



1, 3, 4, 8, 18, 45, 104, 246, 590, 1447, 3582, 8864, 22216, 55989, 141738, 360486, 920892, 2360953, 6073160, 15664216, 40510215, 105017120, 272821646, 710143301, 1851830021, 4836984396, 12653549540, 33148606878, 86954036990, 228373959896, 600482317125, 1580587864193, 4164596465439, 10983396620288
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OFFSET

0,2


LINKS

Robert G. Wilson v, Table of n, a(n) for n = 0..38


FORMULA

a(n) ~ 1/n * e^n * (e1).


EXAMPLE

a(0) = 1 as 2 is the only between 1 and e. a(4) = 18, as there are 18 primes between e^4 = 54.59815... and e^5 = 148.4131591...


MAPLE

# To find all primes between ceiling(base^(n1)) and floor(base^n). This uses the Maple function 'isprime', which is a probabilistic primality testing routine.
base := exp(1); maxx := 15; for n from 1 to maxx do for i from ceil(base^(n1)) to floor(base^(n)) do if (isprime(i)) then numPrimes := numPrimes + 1: end if; od; printf("Number of primes between ceil(%f)^%d and floor(%f)^%d is %d ", base, n1, base, n, numPrimes); od; # Winston C. Yang (winston(AT)cs.wisc.edu), May 17 2001


CROSSREFS

Cf. A061274.
First differences of A040014.
Sequence in context: A192474 A183494 A107429 * A254715 A107328 A065034
Adjacent sequences: A061270 A061271 A061272 * A061274 A061275 A061276


KEYWORD

nonn


AUTHOR

Amarnath Murthy, Apr 25 2001


EXTENSIONS

More terms from Winston C. Yang (winston(AT)cs.wisc.edu), May 17 2001
a(29)a(33) from Robert G. Wilson v, Jun 05 2016


STATUS

approved



