A328405 - OEIS

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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.

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