A329027 The least missing digit in the primorial base expansion of n. Only significant digits are considered, as the leading zeros are ignored.

0, 2, 0, 1, 0, 2, 2, 2, 0, 3, 0, 1, 3, 3, 0, 1, 0, 1, 2, 2, 0, 1, 0, 1, 2, 2, 0, 1, 0, 2, 2, 2, 2, 3, 3, 2, 2, 2, 0, 3, 0, 3, 3, 3, 0, 3, 0, 2, 2, 2, 0, 4, 0, 2, 2, 2, 0, 3, 0, 1, 3, 3, 3, 1, 3, 3, 3, 3, 0, 3, 0, 1, 3, 3, 0, 1, 0, 1, 4, 4, 0, 1, 0, 1, 3, 3, 0, 1, 0, 1, 2, 2, 2, 1, 4, 2, 2, 2, 0, 4, 0, 1, 4, 4, 0

Offset: 1

Author

Antti Karttunen, Nov 03 2019

Keywords

• nonn
• base

Comments

For n = 0 the value is ambiguous, thus the sequence starts from n=1.

Examples

			19 in primorial base (A049345) is written as "301". The least missing digit is 2, thus a(19) = 2.
		

Links

• Antti Karttunen, Table of n, a(n) for n = 1..32768
• Index entries for sequences related to primorial base.

Crossrefs

Cf. A049345, A329028.

Cf. A328574 (after its initial term, gives the positions of zeros in this sequence), A328840 (after its initial term, gives the positions of ones in this 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[0, Max[s]+1], s]]]; Array[a, 100] (* Amiram Eldar, Mar 13 2024 *)

PARI

A329027(n) = { my(m=Map(), p=2); while(n, mapput(m,(n%p),1); n = n\p; p = nextprime(1+p)); for(k=0,oo,if(!mapisdefined(m,k),return(k))); };