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A328398 Maximal digit value in primorial base expansion of A276086(A276086(A276086(n))), where A276086(n) converts primorial base expansion of n into its prime product form.

%I A328398 #25 Oct 18 2019 11:28:26
%S A328398 1,1,2,3,1,7,4,5,7,2,7,12,35,14,11,15,15,11,49,19,88,64,81,403,198,
%T A328398 248,405,271,166,449,2,3,6,7,11,25,5,30,32,3,37,8,66,53,49,49,302,40,
%U A328398 73,116,48,47,177,495,351,391,518,338,188,331,15,16,109,65,13,39,11,37,25,44,371,181,300,87,154,44,440,396,131
%N A328398 Maximal digit value in primorial base expansion of A276086(A276086(A276086(n))), where A276086(n) converts primorial base expansion of n into its prime product form.
%C A328398 2's occur at 2, 9, 30, 2312, 2559, 32589, ... (cf. A143293).
%C A328398 In range n = 0 .. 32768, a(n) attains the maximum possible value A000040(A328406(n))-1 only at n=2 and n=2804, when it must be the value of the most significant digit in the primorial base expansion of A328403(n).
%C A328398 When comparing the scatter plots of this sequence and those of A328389 and A328394, although the overall shape gets more blurred on each iteration of A276086, it is easy to see by informal inductive reasoning that the low values of the sequences should occur at about same positions.
%C A328398 Question: Are there any 1's after a(0), a(1) and a(4)?
%H A328398 Antti Karttunen, <a href="/A328398/b328398.txt">Table of n, a(n) for n = 0..32768</a>
%H A328398 <a href="/index/Pri#primorialbase">Index entries for sequences related to primorial base</a>
%F A328398 a(n) = A328114(A328403(n)) = A328389(A276087(n)) = A328394(A276086(n)).
%F A328398 For all n, a(n) < A000040(A328406(n)).
%t A328398 Block[{b = MixedRadix[Reverse@ Prime@ Range@ 120], f}, f[n_] := Times @@ Power @@@ # &@ Transpose@{Prime@ Range@ Length@ #, Reverse@ #} &@ IntegerDigits[n, b]; Array[Max@ IntegerDigits[Nest[f, #, 3], b] &, 79, 0]] (* _Michael De Vlieger_, Oct 17 2019 *)
%o A328398 (PARI)
%o A328398 A276086(n) = { my(m=1, p=2); while(n, m *= (p^(n%p)); n = n\p; p = nextprime(1+p)); (m); };
%o A328398 A328114(n) = { my(s=0, p=2); while(n, s = max(s,n%p); n = n\p; p = nextprime(1+p)); (s); };
%o A328398 A328398(n) = A328114(A276086(A276086(A276086(n))));
%Y A328398 Cf. A002110, A143293, A276086, A276087, A328114, A328389, A328394, A328403, A328406.
%K A328398 nonn
%O A328398 0,3
%A A328398 _Antti Karttunen_, Oct 16 2019