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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.

%I A376407 #9 Nov 08 2024 17:58:23
%S A376407 0,1,3,9,23,353,10519,12086209,1174153011340170531,
%T A376407 73582975079922326904310062621361286634299329277087298285
%N 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.
%C A376407 a(10) has 272 digits and a(11) has 1523 digits.
%C A376407 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.
%H A376407 Antti Karttunen, <a href="/A376407/b376407.txt">Table of n, a(n) for n = 0..10</a>
%H A376407 <a href="/index/Bi#binary">Index entries for sequences related to binary expansion of n</a>
%F A376407 a(n) = A048675(A376406(n)).
%F A376407 a(0) = 0; and for n > 0, a(n) = a(n-1) + A376406(n-1) = Sum_{i=0..n-1} A376406(i).
%o A376407 (PARI)
%o A376407 A019565(n) = { my(m=1, p=1); while(n>0, p = nextprime(1+p); if(n%2, m *= p); n >>= 1); (m); };
%o A376407 A376407(n) = if(!n,0,my(x=A376407(n-1)); x+A019565(x));
%Y A376407 Cf. A019565, A048675, A376406, A376409.
%Y A376407 Cf. also A376403 (an analogous sequence for A276076).
%K A376407 nonn
%O A376407 0,3
%A A376407 _Antti Karttunen_, Nov 04 2024