A328404 The length of primorial base expansion (number of significant digits) of A276086(n), where A276086(n) converts primorial base expansion of n into its prime product form.

1, 2, 2, 3, 3, 3, 2, 3, 3, 4, 4, 4, 3, 4, 4, 4, 5, 5, 4, 5, 5, 5, 5, 5, 5, 5, 5, 6, 6, 6, 3, 3, 3, 4, 4, 4, 4, 4, 4, 5, 5, 5, 4, 5, 5, 5, 5, 6, 5, 5, 6, 6, 6, 6, 6, 6, 6, 6, 7, 7, 4, 4, 4, 5, 5, 5, 5, 5, 5, 5, 5, 6, 5, 6, 6, 6, 6, 6, 6, 6, 6, 7, 7, 7, 7, 7, 7, 7, 7, 8, 5, 5, 5, 5, 6, 6, 5, 6, 6, 6, 6, 7, 6, 6, 6, 7

Offset

0,2

Comments

a(n) is the least k such that A002110(k) > A276086(n). - Antti Karttunen, Jan 06 2026

Links

Antti Karttunen, Table of n, a(n) for n = 0..32768

Index entries for sequences related to primorial base.

Formula

a(n) = A235224(A276086(n)) = A061395(A276087(n)).

For all n, a(A143293(n-1)) = n+1.

For all n, A000040(a(n)) > A328389(n).

Mathematica

Block[{b = MixedRadix[Reverse@ Prime@ Range@ 120]}, Array[IntegerLength[Times @@ Power @@@ # &@ Transpose@ {Prime@ Range@ Length@ #, Reverse@ #} &@ IntegerDigits[#, b], b] &, 105, 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); };
A328404(n) = A235224(A276086(n));
(PARI)
A276086(n) = { my(m=1, p=2); while(n, m *= (p^(n%p)); n = n\p; p = nextprime(1+p)); (m); };
A328404(n) = { my(x=A276086(n), m=1); for(k=1, oo, m *= prime(k); if(m>x, return(k))); }; \\ Antti Karttunen, Jan 06 2026

Crossrefs

Cf. A002110, A061395, A143293, A235224, A276086, A276087, A328389, A328405, A328406, A391936.

Cf. A328402 (number of times each n occurs in this sequence).

Sequence in context: A332252 A238268 A194883 * A175453 A014499 A055778

Adjacent sequences: A328401 A328402 A328403 * A328405 A328406 A328407

Keyword

nonn

Author

Antti Karttunen, Oct 16 2019

Status

approved