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.

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

Offset: 0

Author

Antti Karttunen, Nov 04 2024

Keywords

• nonn

Comments

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.

Links

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

Crossrefs

Cf. A019565, A048675, A376406, A376409.

Cf. also A376403 (an analogous sequence 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); };
A376407(n) = if(!n,0,my(x=A376407(n-1)); x+A019565(x));

Formula

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).