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

0,6

Links

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

Index entries for sequences related to primorial base.

Formula

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

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

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 *)

Prog

(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));

Crossrefs

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

Cf. A049345, A276086, A351563, A351566.

Sequence in context: A115861 A282355 A199322 * A284203 A341594 A368774

Adjacent sequences: A351564 A351565 A351566 * A351568 A351569 A351570

Keyword

nonn,base

Author

Antti Karttunen, Apr 01 2022

Status

approved