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A328405 The length of primorial base expansion (number of significant digits) of A276086(A276086(n)), where A276086(n) converts primorial base expansion of n into its prime product form.

%I A328405 #10 Oct 18 2019 21:28:41
%S A328405 2,2,3,2,4,4,3,4,4,3,5,5,5,6,6,6,5,5,7,6,9,8,10,14,11,12,14,12,12,15,
%T A328405 3,4,5,4,5,6,4,5,7,3,8,5,9,9,8,7,12,7,8,12,8,7,12,14,16,15,15,15,11,
%U A328405 12,5,6,8,7,7,8,5,7,9,9,14,12,12,9,12,7,15,15,12,12,18,13,20,17,11,13,15,14,17,13,8,9,11,14,11,13,11,10,10,10
%N A328405 The length of primorial base expansion (number of significant digits) of A276086(A276086(n)), where A276086(n) converts primorial base expansion of n into its prime product form.
%H A328405 Antti Karttunen, <a href="/A328405/b328405.txt">Table of n, a(n) for n = 0..32768</a>
%H A328405 <a href="/index/Pri#primorialbase">Index entries for sequences related to primorial base</a>
%F A328405 a(n) = A235224(A276087(n)) = A061395(A328403(n)).
%F A328405 For all n, A000040(a(n)) > A328394(n).
%t A328405 Block[{b = MixedRadix[Reverse@ Prime@ Range@ 120], f}, f[n_] := Times @@ Power @@@ # &@ Transpose@ {Prime@ Range@ Length@ #, Reverse@ #} &@ IntegerDigits[n, b]; Array[IntegerLength[Nest[f, #, 2], b] &, 100, 0]] (* _Michael De Vlieger_, Oct 17 2019 *)
%o A328405 (PARI)
%o A328405 A235224(n) = { my(s=0, p=2); while(n, s++; n = n\p; p = nextprime(1+p)); (s); };
%o A328405 A276086(n) = { my(m=1, p=2); while(n, m *= (p^(n%p)); n = n\p; p = nextprime(1+p)); (m); };
%o A328405 A276087(n) = A276086(A276086(n));
%o A328405 A328405(n) = A235224(A276087(n));
%Y A328405 Cf. A061395, A143293, A235224, A276086, A276087, A328394, A328403, A328404, A328406.
%K A328405 nonn
%O A328405 0,1
%A A328405 _Antti Karttunen_, Oct 16 2019