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A328406 The length of primorial base expansion (number of significant digits) of A276086(A276086(A276086(n))), where A276086(n) converts primorial base expansion of n into its prime product form.

%I A328406 #12 Oct 18 2019 11:29:21
%S A328406 2,3,2,3,3,7,4,5,6,3,7,8,12,8,7,12,12,7,17,11,25,21,24,84,49,63,94,67,
%T A328406 49,97,4,6,8,9,7,10,6,14,13,4,14,11,22,22,19,20,66,16,23,40,20,19,50,
%U A328406 105,81,87,104,71,49,81,12,10,34,21,9,16,11,23,16,17,85,49,71,27,44,21,93,87,39,58,171,50,205,112,54,78,78
%N A328406 The length of primorial base expansion (number of significant digits) of A276086(A276086(A276086(n))), where A276086(n) converts primorial base expansion of n into its prime product form.
%H A328406 Antti Karttunen, <a href="/A328406/b328406.txt">Table of n, a(n) for n = 0..32768</a>
%H A328406 <a href="/index/Pri#primorialbase">Index entries for sequences related to primorial base</a>
%F A328406 a(n) = A235224(A328403(n)) = A328404(A276087(n)) = A328405(A276086(n)).
%F A328406 For all n, A000040(a(n)) > A328398(n).
%t A328406 Block[{b = MixedRadix[Reverse@ Prime@ Range@ 120], f}, f[n_] := Times @@ Power @@@ # &@ Transpose@ {Prime@ Range@ Length@ #, Reverse@ #} &@ IntegerDigits[n, b]; Array[IntegerLength[Nest[f, #, 3], b] &, 87, 0]] (* _Michael De Vlieger_, Oct 17 2019 *)
%o A328406 (PARI)
%o A328406 A235224(n) = { my(s=0, p=2); while(n, s++; n = n\p; p = nextprime(1+p)); (s); };
%o A328406 A276086(n) = { my(m=1, p=2); while(n, m *= (p^(n%p)); n = n\p; p = nextprime(1+p)); (m); };
%o A328406 A328403(n) = A276086(A276086(A276086(n)));
%o A328406 A328406(n) = A235224(A328403(n));
%Y A328406 Cf. A235224, A276086, A276087, A328398, A328403, A328404, A328405.
%K A328406 nonn
%O A328406 0,1
%A A328406 _Antti Karttunen_, Oct 16 2019