

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.


6



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, 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, 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
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OFFSET

0,1


LINKS

Antti Karttunen, Table of n, a(n) for n = 0..32768
Index entries for sequences related to primorial base


FORMULA

a(n) = A235224(A276087(n)) = A061395(A328403(n)).
For all n, A000040(a(n)) > A328394(n).


MATHEMATICA

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 *)


PROG

(PARI)
A235224(n) = { my(s=0, p=2); while(n, s++; n = n\p; p = nextprime(1+p)); (s); };
A276086(n) = { my(m=1, p=2); while(n, m *= (p^(n%p)); n = n\p; p = nextprime(1+p)); (m); };
A276087(n) = A276086(A276086(n));
A328405(n) = A235224(A276087(n));


CROSSREFS

Cf. A061395, A143293, A235224, A276086, A276087, A328394, A328403, A328404, A328406.
Sequence in context: A209700 A115980 A088936 * A049822 A140060 A164341
Adjacent sequences: A328402 A328403 A328404 * A328406 A328407 A328408


KEYWORD

nonn


AUTHOR

Antti Karttunen, Oct 16 2019


STATUS

approved



