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.

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, 248, 405, 271, 166, 449, 2, 3, 6, 7, 11, 25, 5, 30, 32, 3, 37, 8, 66, 53, 49, 49, 302, 40, 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

Offset: 0

Author

Antti Karttunen, Oct 16 2019

Keywords

• nonn

Comments

2's occur at 2, 9, 30, 2312, 2559, 32589, ... (cf. A143293).

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).

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.

Question: Are there any 1's after a(0), a(1) and a(4)?

Links

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

Crossrefs

Cf. A002110, A143293, A276086, A276087, A328114, A328389, A328394, A328403, A328406.

Programs

Mathematica

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 *)

PARI

A276086(n) = { my(m=1, p=2); while(n, m *= (p^(n%p)); n = n\p; p = nextprime(1+p)); (m); };
A328114(n) = { my(s=0, p=2); while(n, s = max(s,n%p); n = n\p; p = nextprime(1+p)); (s); };
A328398(n) = A328114(A276086(A276086(A276086(n))));

Formula

a(n) = A328114(A328403(n)) = A328389(A276087(n)) = A328394(A276086(n)).

For all n, a(n) < A000040(A328406(n)).