A376409 -id:A376409 - cp's OEIS frontend

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

Antti Karttunen, Nov 04 2024

nonn

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.

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

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).

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));

A376407 a(0) = 0, and for n > 0, a(n) = a(n-1) + A019565(a(n-1)), where A019565 is the base-2 exp-function.

Original entry on oeis.org

0, 1, 3, 9, 23, 353, 10519, 12086209, 1174153011340170531, 73582975079922326904310062621361286634299329277087298285

Offset: 0

Antti Karttunen, Nov 04 2024

nonn

a(10) has 272 digits and a(11) has 1523 digits.

By induction, it is easy to see that formula a(n) = A048675(A376406(n)) implies that from the second term onward, this sequence gives the partial sums of A376406. See comments and examples in that sequence.

Antti Karttunen, Table of n, a(n) for n = 0..10
Index entries for sequences related to binary expansion of n

Cf. A019565, A048675, A376406, A376409.

Cf. also A376403 (an analogous sequence for A276076).

A019565(n) = { my(m=1, p=1); while(n>0, p = nextprime(1+p); if(n%2, m *= p); n >>= 1); (m); };
A376407(n) = if(!n,0,my(x=A376407(n-1)); x+A019565(x));

a(n) = A048675(A376406(n)).

a(0) = 0; and for n > 0, a(n) = a(n-1) + A376406(n-1) = Sum_{i=0..n-1} A376406(i).

cp's OEIS Frontend

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.

Views

Author

Keywords

Comments

Links

Crossrefs

Programs

PARI