A217884 Let c(m)=prime(m), m=1,2,3,4. For m>=5, suppose that c(m)/e is in the interval [c(k),c(k+1)). Then let c(m+1)=e*c(k+1) if e*c(k+1) < prime(m+1), and otherwise let c(m+1) = prime(m+1). Then a(n) is the n-th prime in {c(m)}.

2, 3, 5, 7, 13, 19, 31, 43, 47, 67, 71, 73, 79, 83, 103, 107, 109, 113, 137, 139, 157, 163, 173, 179, 181, 197, 211, 229, 239, 241, 251, 257, 269, 271, 283, 313, 317, 337, 347, 353, 359, 367, 397, 401, 409, 419

Offset: 1

Author

Vladimir Shevelev, Oct 14 2012

Keywords

• nonn

Comments

The preliminary sequence begins 2,3,5,7,3*e,13,5*e,19,7*e,3*e^2,31,...

with terms of the form p*e^k, where p is prime, k>=0.

Crossrefs

Cf. A217689, A217691.

Formula

If A(n)is the number of terms not exceeding n, then heuristically A(n)~pi(n). Practically, an approximation is given by formula A(n) ~ n/log(n*log(n)).

Extensions

Terms a(1)-a(20) confirmed and terms a(21)-a(46) added by John W. Layman, Oct 24 2012