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

1,2

Comments

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

Links

Antti Karttunen, Table of n, a(n) for n = 1..32768

Index entries for sequences related to primorial base.

Example

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

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 *)

Prog

(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))); };

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).

Sequence in context: A029397 A129447 A125079 * A235987 A104597 A182936

Adjacent sequences: A329024 A329025 A329026 * A329028 A329029 A329030

Keyword

nonn,base

Author

Antti Karttunen, Nov 03 2019

Status

approved