A351567 The second least significant nonzero digit in the primorial base expansion of n, or 0 if there is no such digit.

0, 0, 0, 1, 0, 2, 0, 1, 1, 1, 1, 2, 0, 2, 2, 1, 2, 2, 0, 3, 3, 1, 3, 2, 0, 4, 4, 1, 4, 2, 0, 1, 1, 1, 1, 2, 1, 1, 1, 1, 1, 2, 1, 2, 2, 1, 2, 2, 1, 3, 3, 1, 3, 2, 1, 4, 4, 1, 4, 2, 0, 2, 2, 1, 2, 2, 2, 1, 1, 1, 1, 2, 2, 2, 2, 1, 2, 2, 2, 3, 3, 1, 3, 2, 2, 4, 4, 1, 4, 2, 0, 3, 3, 1, 3, 2, 3, 1, 1, 1, 1, 2, 3, 2, 2, 1

Offset: 0

Author

Antti Karttunen, Apr 01 2022

Keywords

• nonn
• base

Links

• Antti Karttunen, Table of n, a(n) for n = 0..60060
• Index entries for sequences related to primorial base.

Crossrefs

Cf. A060735 (gives the positions of zeros after a(0)=0).

Cf. A049345, A276086, A351563, A351566.

Programs

Mathematica

a[n_] := Module[{k = n, p = 2, s = {}, r}, While[{k, r} = QuotientRemainder[k, p]; k != 0 || r != 0, If[r > 0, AppendTo[s, r]]; p = NextPrime[p]]; i = Position[s, ?(# > 0 &)] // Flatten; If[Length[s] < 2, 0, s[[2]]]]; Array[a, 100, 0] (* _Amiram Eldar, Mar 13 2024 *)

PARI

A351563(n) = if(1>=omega(n), 0, (factor(n))[2,2]);
A276086(n) = { my(m=1, p=2); while(n, m *= (p^(n%p)); n = n\p; p = nextprime(1+p)); (m); };
A351567(n) = A351563(A276086(n));

Formula

a(n) = A351563(A276086(n)).

For all n, a(n) < A351566(n).