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

Offset: 0

Author

Antti Karttunen, Oct 16 2019

Keywords

• nonn

Links

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

Crossrefs

Cf. A061395, A143293, A235224, A276086, A276087, A328394, A328403, A328404, A328406.

Programs

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 *)

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));

Formula

a(n) = A235224(A276087(n)) = A061395(A328403(n)).

For all n, A000040(a(n)) > A328394(n).