A061273 - OEIS

%I #23 May 03 2023 19:02:09

%S 1,3,4,8,18,45,104,246,590,1447,3582,8864,22216,55989,141738,360486,

%T 920892,2360953,6073160,15664216,40510215,105017120,272821646,

%U 710143301,1851830021,4836984396,12653549540,33148606878,86954036990,228373959896,600482317125,1580587864193,4164596465439,10983396620288

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

%H Robert G. Wilson v, <a href="/A061273/b061273.txt">Table of n, a(n) for n = 0..38</a>

%F a(n) ~ 1/n * e^n * (e-1).

%e 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...

%p # To find all primes between ceiling(base^(n-1)) and floor(base^n). This uses the Maple function 'isprime', which is a probabilistic primality testing routine.

%p base := exp(1); maxx := 15; for n from 1 to maxx do for i from ceil(base^(n-1)) 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, n-1, base, n, numPrimes); od; # Winston C. Yang (winston(AT)cs.wisc.edu), May 17 2001

%t Differences[PrimePi[#]&/@(E^Range[0,35])] (* _Harvey P. Dale_, May 03 2023 *)

%Y Cf. A061274.

%Y First differences of A040014.

%K nonn

%O 0,2

%A _Amarnath Murthy_, Apr 25 2001

%E More terms from Winston C. Yang (winston(AT)cs.wisc.edu), May 17 2001

%E a(29)-a(33) from _Robert G. Wilson v_, Jun 05 2016