A376408 a(0) = 1, and for n > 0, a(n) = a(n-1) * A019565(a(n-1)), where A019565 is the base-2 exp-function.

1, 2, 6, 90, 353430, 274407373885179150, 2443417474326613595267894539584266773823049253134356678751627846400290750

Offset: 0

Author

Antti Karttunen, Nov 04 2024

Keywords

• nonn

Comments

a(7) has 407 digits, and a(8) has 2804 digits.

Like A376406, this satisfies A048675(a(n)) = a(n-1) + A048675(a(n-1)), for all n >= 1, that is, applying A048675 to the terms gives the partial sums shifted right once, A376409. However, unlike A376406, this is not a subsequence of A005117: a(3) = 90 is the first term that is not squarefree. Neither can we say that this is the lexicographically largest of such sequences, as there are also infinite sequences that begin as 1, 2, 6, 120, 38, ... or as 1, 2, 6, 120, 2042040, ... that satisfy the same condition.

Links

• Antti Karttunen, Table of n, a(n) for n = 0..7
• Index entries for sequences related to binary expansion of n

Crossrefs

Cf. A019565, A048675, A376406.

Cf. A376409 (= A048675(a(n)), also partial sums from its second term onward).

Cf. also analogous sequences A002110 (for A276086) and A376400 (for A276076).

Programs

PARI

A019565(n) = { my(m=1, p=1); while(n>0, p = nextprime(1+p); if(n%2, m *= p); n >>= 1); (m); };
A376408(n) = if(!n,1,my(x=A376408(n-1)); x*A019565(x));