cp's OEIS Frontend

a(7) has 9971 digits and is too large to include. - Jason Yuen, Aug 30 2025

A050809 is a subset. Lim_{n --> infinity} a(n+1)/a(n) = e. - Jonathan Vos Post, May 02 2006

Semiprime analog of A074496 = first prime after e^n. Lim_{n->infinity} a(n+1)/a(n) = e. There are numbers where floor(e^n) is itself a semiprime, as with floor(e^6) = 403 = 13 * 31, floor(e^15) = 3269017 = 773 * 4229, floor(e^20) = 485165195 = 5 * 97033039, floor(e^22) = 3584912846 = 2 * 1792456423, floor(e^24) = 26489122129 = 103 * 257175943.

Intersection of A000040 and A061675.

The next term has 1535 digits. - Harvey P. Dale, Apr 26 2011

Pi and semiprime analog of A074496 First prime after e^n. Lim_{n->infinity} a(n+1)/a(n) = Pi. See also A000796 Decimal expansion of Pi. There are numbers where floor(Pi^n) is itself a semiprime, as with floor(Pi^2) = 9, floor(Pi^6) = 961 = 31^2, floor(Pi^9) = 29809 = 13 * 2293, floor(Pi^25) = 2683779414317 = 5749 * 466825433.

Explicitly, abs( e^k - (prevprime(e^k)+nextprime(e^k))/2 ) < 1.

For k>1, the formula (prevprime(e^k)+nextprime(e^k))/2 either gives floor(e^k), for k = 61, 74, 2170, ..., or gives ceiling(e^k), for k = 3, 16, 91, 113, 1441, 1566, 2499, ... This partitions {a(n)}\{1} into two subsequences each of which can be conjectured to have relative density 1/2.

In cases k = 16, 61, 113, 2499, ... the distance is actually less than 0.5. Then the formula (prevprime(e^k)+nextprime(e^k))/2 yields round(e^k), the nearest integer to e^k.