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

%I A329028 #16 Mar 13 2024 01:51:00
%S A329028 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,
%T A329028 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,
%U A329028 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
%N A329028 The least missing nonzero digit in the primorial base expansion of n.
%H A329028 Antti Karttunen, <a href="/A329028/b329028.txt">Table of n, a(n) for n = 0..32786</a>
%H A329028 <a href="/index/Pri#primorialbase">Index entries for sequences related to primorial base</a>.
%F A329028 a(n) = A134193(A276086(n)) = A257993(A328835(n)).
%F A329028 a(A276086(n)) = A329030(n).
%e A329028 19 in primorial base (A049345) is written as "301". The least missing nonzero digit is 2, thus a(19) = 2.
%e A329028 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.
%t A329028 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 *)
%o A329028 (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))); };
%Y A329028 Cf. A049345, A134193, A257993, A276086, A328835, A329027, A329030.
%Y A329028 Cf. A328840 (the positions of ones in this sequence).
%Y A329028 Cf. A257079 for analogous sequence.
%K A329028 nonn,base
%O A329028 0,2
%A A329028 _Antti Karttunen_, Nov 03 2019