A329028 The least missing nonzero digit in the primorial base expansion of n.

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

Offset: 0

Author

Antti Karttunen, Nov 03 2019

Keywords

• nonn
• base

Examples

			19 in primorial base (A049345) is written as "301". The least missing nonzero digit is 2, thus a(19) = 2.
809 in primorial base is written as "35421". The least missing nonzero digit is 6, thus a(809) = 6, and this is also the first position where 6 appears in this sequence.
		

Links

• Antti Karttunen, Table of n, a(n) for n = 0..32786
• Index entries for sequences related to primorial base.

Crossrefs

Cf. A049345, A134193, A257993, A276086, A328835, A329027, A329030.

Cf. A328840 (the positions of ones in this sequence).

Cf. A257079 for analogous sequence.

Programs

Mathematica

a[n_] := Module[{k = n, p = 2, s = {}, r}, While[{k, r} = QuotientRemainder[k, p]; k != 0 || r != 0, AppendTo[s, r]; p = NextPrime[p]]; Min[Complement[Range[Max[s] + 1], s]]]; a[0] = 1; Array[a, 100, 0] (* Amiram Eldar, Mar 13 2024 *)

PARI

A329028(n) = { my(m=Map(), p=2); while(n, mapput(m,(n%p),1); n = n\p; p = nextprime(1+p)); for(k=1,oo,if(!mapisdefined(m,k),return(k))); };

Formula

a(n) = A134193(A276086(n)) = A257993(A328835(n)).

a(A276086(n)) = A329030(n).