A061273 Number of primes between successive powers of e (= 2.718281828...).
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
Offset: 0
Keywords
Examples
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...
Links
- Robert G. Wilson v, Table of n, a(n) for n = 0..38
Programs
-
Maple
# 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. 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 -
Mathematica
Differences[PrimePi[#]&/@(E^Range[0,35])] (* Harvey P. Dale, May 03 2023 *)
Formula
a(n) ~ 1/n * e^n * (e-1).
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