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

0,2

Links

Antti Karttunen, Table of n, a(n) for n = 0..32786

Index entries for sequences related to primorial base.

Formula

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

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

Example

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.

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 *)

Prog

(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))); };

Crossrefs

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

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

Cf. A257079 for analogous sequence.

Sequence in context: A194326 A295277 A194290 * A257079 A327567 A260372

Adjacent sequences: A329025 A329026 A329027 * A329029 A329030 A329031

Keyword

nonn,base

Author

Antti Karttunen, Nov 03 2019

Status

approved