A376400 a(0) = 1, and for n > 0, a(n) = a(n-1) * A276076(a(n-1)), where A276076 is the factorial base exp-function.

1, 2, 6, 30, 1050, 70814493750, 7568077812763134673885891483463343434987134201379042046671543939118568739667281250

Offset: 0

Author

Antti Karttunen, Nov 02 2024

Keywords

• nonn

Comments

a(7) has 2129 (decimal) digits.

Like A376399, this satisfies A276075(a(n)) = a(n-1) + A276075(a(n-1)), for all n >= 1, so also here, applying A276075 to the terms gives the partial sums shifted right once, A376401.

However, unlike A376399, this is not a subsequence of A276078: a(5) = 70814493750 is the first term that is in A276079.

Links

• Index entries for sequences related to factorial base representation

Crossrefs

Cf. A276075, A276076, A276078, A276079, A376399, A376403.

Cf. A376401 (= A276075(a(n)), also gives the partial sums from its second term onward).

Cf. also analogous sequences A002110 (for A276086) and A376408 (for A019565).

Programs

PARI

A276076(n) = { my(m=1, p=2, i=2); while(n, m *= (p^(n%i)); n = n\i; p = nextprime(1+p); i++); (m); };
A376400(n) = if(!n,1,my(x=A376400(n-1)); x*A276076(x));