OFFSET
0,2
LINKS
Robert G. Wilson v, Table of n, a(n) for n = 0..38
FORMULA
a(n) ~ 1/n * e^n * (e-1).
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^(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 *)
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