A351566 Radix of the second least significant nonzero digit in the primorial base expansion of n, or 1 if there is no such digit.

1, 1, 1, 3, 1, 3, 1, 5, 5, 3, 5, 3, 1, 5, 5, 3, 5, 3, 1, 5, 5, 3, 5, 3, 1, 5, 5, 3, 5, 3, 1, 7, 7, 3, 7, 3, 7, 5, 5, 3, 5, 3, 7, 5, 5, 3, 5, 3, 7, 5, 5, 3, 5, 3, 7, 5, 5, 3, 5, 3, 1, 7, 7, 3, 7, 3, 7, 5, 5, 3, 5, 3, 7, 5, 5, 3, 5, 3, 7, 5, 5, 3, 5, 3, 7, 5, 5, 3, 5, 3, 1, 7, 7, 3, 7, 3, 7, 5, 5, 3, 5, 3, 7, 5, 5, 3

Offset: 0

Author

Antti Karttunen, Apr 01 2022

Keywords

• nonn
• base

Comments

The terms larger than one are given by the k-th prime (A000040), where k is the position of the second least significant nonzero digit in the primorial base expansion of n, counted from the right. See the example.

Examples

			For n = 13, its primorial base representation (see A049345) is "201" as 13 = 2*A002110(2) + 1*A002110(0). The one-based index of the second least significant nonzero digit ("2"), when counted from the right, is 3, therefore a(13) = A000040(3) = 5.
		

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 ones after the initial one at a(0)=1).

Cf. A000040, A002110, A049345, A053669, A119288, A276086, A351567.

Programs

Mathematica

a[n_] := Module[{k = n, p = 2, s = {}, r, i}, While[{k, r} = QuotientRemainder[k, p]; k != 0 || r != 0, AppendTo[s, r]; p = NextPrime[p]]; i = Position[s, ?(# > 0 &)] // Flatten; If[Length[i] < 2, 1, Prime[i[[2]]]]]; Array[a, 100, 0] (* _Amiram Eldar, Mar 13 2024 *)

PARI

A119288(n) = if(1>=omega(n), 1, (factor(n))[2,1]);
A276086(n) = { my(m=1, p=2); while(n, m *= (p^(n%p)); n = n\p; p = nextprime(1+p)); (m); };
A351566(n) = A119288(A276086(n));

Formula

a(n) = A119288(A276086(n)).

For all n, a(n) > A351567(n).

If a(n) > 1, then a(n) > A053669(n).