0,2

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

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

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...

# 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

Differences[PrimePi[#]&/@(E^Range[0, 35])] (* Harvey P. Dale, May 03 2023 *)

Cf. A061274.

First differences of A040014.

Sequence in context: A183494 A107429 A372489 * A254715 A107328 A065034

Adjacent sequences: A061270 A061271 A061272 * A061274 A061275 A061276

Amarnath Murthy, Apr 25 2001

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

approved