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

0,4

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.

Links

Antti Karttunen, Table of n, a(n) for n = 0..60060

Index entries for sequences related to primorial base.

Formula

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

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

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

Example

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.

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 *)

Prog

(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));

Crossrefs

Cf. A060735 (gives the positions of ones after the initial one at a(0)=1).

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

Sequence in context: A013603 A157892 A264441 * A346241 A328573 A369066

Adjacent sequences: A351563 A351564 A351565 * A351567 A351568 A351569

Keyword

nonn,base

Author

Antti Karttunen, Apr 01 2022

Status

approved