A321340 a(1) = 1; thereafter a(n) = a(n-1) * prime(n-1)^a(n-1).

1, 2, 18, 68664550781250

Offset: 1

Author

Russell Y. Webb, Nov 05 2018

Keywords

• nonn

Comments

The prime factorization of a(n) describes all previous terms in the sequence: a(n) = prime(1)^a(1) * prime(2)^a(2) * prime(3)^a(3) * ...* prime(n-1)^a(n-1).

An infinite and monotonically increasing sequence which grows very rapidly.

Examples

			68664550781250 = 2 * 3^2 * 5^18 = prime(1)^1 * prime(2)^2 * prime(3)^18.
		

Crossrefs

Somewhat similar to A007097.

Cf. A321339.

Programs

Mathematica

Nest[Append[#, #[[-1]] Prime[Length@ #]^#[[-1]] ] &, {1}, 3] (* Michael De Vlieger, Nov 05 2018 *)

PARI

apply( ppp(n) = prod(i=1, n-1, prime(i)^ppp(i)), [1..4] )