A328828 Index of the least significant digit larger than one in the primorial base expansion of n, 0 if no such digit exists.

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

Offset: 0

Author

Antti Karttunen, Oct 29 2019

Keywords

• nonn
• base

Links

• Antti Karttunen, Table of n, a(n) for n = 0..65537
• Index entries for sequences related to primorial base.

Crossrefs

Cf. A000720, A049345, A055396, A276086, A276156 (positions of 0's), A277885, A328572, A328829 [= a(A276086(n))], A328832, A381032 [= A008578(1+a(n))].

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 = FirstPosition[s, ?(# > 1 &)]; If[MissingQ[i], 0, i[[1]]]]; Array[a, 100] (* _Amiram Eldar, Mar 13 2024 *)

PARI

A328828(n) = { my(i=1, p=2); while(n, if((n%p)>1, return(i)); i++; n = n\p; p = nextprime(1+p)); (0); };

Formula

a(n) = A277885(A276086(n)) = A055396(A328572(n)).

a(n) = A000720(A381032(n)). - Antti Karttunen, Feb 23 2025