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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. 7

%I

%S 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 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 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 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 Antti Karttunen, <a href="/A328406/b328406.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(A328403(n)) = A328404(A276087(n)) = A328405(A276086(n)).

%F For all n, A000040(a(n)) > A328398(n).

%t 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 (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 A328403(n) = A276086(A276086(A276086(n)));

%o A328406(n) = A235224(A328403(n));

%Y Cf. A235224, A276086, A276087, A328398, A328403, A328404, A328405.

%K nonn

%O 0,1

%A _Antti Karttunen_, Oct 16 2019

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Last modified December 9 03:27 EST 2019. Contains 329872 sequences. (Running on oeis4.)