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

1, 2, 18, 68664550781250

Offset

1,2

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.

Links

Table of n, a(n) for n=1..4.

Example

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

Mathematica

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

Prog

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

Crossrefs

Somewhat similar to A007097.

Cf. A321339.

Sequence in context: A293242 A321339 A086367 * A221229 A221602 A354207

Adjacent sequences: A321337 A321338 A321339 * A321341 A321342 A321343

Keyword

nonn

Author

Russell Y. Webb, Nov 05 2018

Status

approved