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%I #12 Oct 18 2019 11:29:37
%S 1,2,2,3,3,3,2,3,3,4,4,4,3,4,4,4,5,5,4,5,5,5,5,5,5,5,5,6,6,6,3,3,3,4,
%T 4,4,4,4,4,5,5,5,4,5,5,5,5,6,5,5,6,6,6,6,6,6,6,6,7,7,4,4,4,5,5,5,5,5,
%U 5,5,5,6,5,6,6,6,6,6,6,6,6,7,7,7,7,7,7,7,7,8,5,5,5,5,6,6,5,6,6,6,6,7,6,6,6,7
%N The length of primorial base expansion (number of significant digits) of A276086(n), where A276086(n) converts primorial base expansion of n into its prime product form.
%H Antti Karttunen, <a href="/A328404/b328404.txt">Table of n, a(n) for n = 0..32768</a>
%H <a href="/index/Pri#primorialbase">Index entries for sequences related to primorial base</a>
%F a(n) = A235224(A276086(n)) = A061395(A276087(n)).
%F For all n, a(A143293(n-1)) = n+1.
%F For all n, A000040(a(n)) > A328389(n).
%t Block[{b = MixedRadix[Reverse@ Prime@ Range@ 120]}, Array[IntegerLength[Times @@ Power @@@ # &@ Transpose@ {Prime@ Range@ Length@ #, Reverse@ #} &@ IntegerDigits[#, b], b] &, 105, 0]] (* _Michael De Vlieger_, Oct 17 2019 *)
%o (PARI)
%o A235224(n) = { my(s=0, p=2); while(n, s++; n = n\p; p = nextprime(1+p)); (s); };
%o A276086(n) = { my(m=1, p=2); while(n, m *= (p^(n%p)); n = n\p; p = nextprime(1+p)); (m); };
%o A328404(n) = A235224(A276086(n));
%Y Cf. A061395, A143293, A235224, A276086, A276087, A328389, A328405, A328406.
%Y Cf. A328402 (number of times each n occurs in this sequence).
%K nonn
%O 0,2
%A _Antti Karttunen_, Oct 16 2019
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