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A328316 Iterates of A276086 starting from 0.

%I A328316 #33 Jul 20 2025 15:01:58
%S A328316 0,1,2,3,6,5,18,125,43218,258413198822535882125
%N A328316 Iterates of A276086 starting from 0.
%C A328316 The unique infinite sequence such that a(0) = 0, a(n) = A276085(a(n+1)) for n >= 0, and A129251(a(n)) = 0 for n >= 1, i.e., all nonzero terms must be in A048103.
%C A328316 a(10) is 240 decimal digits long (can be found in b-file), and a(11) is too big to fit even into a b-file as it is 32700 decimal digits long, but it can be found in the given a-file.
%H A328316 Antti Karttunen, <a href="/A328316/b328316.txt">Table of n, a(n) for n = 0..10</a>
%H A328316 Antti Karttunen, <a href="/A328316/a328316.txt">Terms a(0) .. a(11), without running index</a>
%H A328316 <a href="/index/Pri#primorialbase">Index entries for sequences related to primorial base</a>
%F A328316 a(0) = 0; and for n > 0, a(n) = A276086(a(n-1)).
%t A328316 A276086[n0_] := Module[{m = 1, i = 1, n = n0, p}, While[n > 0, p = Prime[i]; m *= p^Mod[n, p]; n = Quotient[n, p]; i++]; m];
%t A328316 NestList[A276086, 0, 10] (* _Jean-François Alcover_, Dec 01 2021, after _Antti Karttunen_ in A276086 *)
%o A328316 (PARI)
%o A328316 A276086(n) = { my(m=1, p=2); while(n, m *= (p^(n%p)); n = n\p; p = nextprime(1+p)); (m); };
%o A328316 A328316(n) = if(!n,0,A276086(A328316(n-1)));
%Y A328316 Cf. A002110, A048103, A129251, A276085, A276086, A328317 (the smallest prime not dividing a(n)), A328318, A328319 (digit sum in primorial base), A328322 (max. digit), A328323.
%Y A328316 Cf. A153013, and also A109162, A179016, A219666, A259934 for more or less analogous sequences.
%Y A328316 Cf. also A328313.
%K A328316 nonn
%O A328316 0,3
%A A328316 _Antti Karttunen_, Oct 14 2019