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

%I #19 Nov 26 2018 17:01:47

%S 1,2,18,68664550781250

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

%C 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).

%C An infinite and monotonically increasing sequence which grows very rapidly.

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

%t Nest[Append[#, #[[-1]] Prime[Length@ #]^#[[-1]] ] &, {1}, 3] (* _Michael De Vlieger_, Nov 05 2018 *)

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

%Y Somewhat similar to A007097.

%Y Cf. A321339.

%K nonn

%O 1,2

%A _Russell Y. Webb_, Nov 05 2018

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Last modified May 20 01:36 EDT 2024. Contains 372703 sequences. (Running on oeis4.)