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A329028
The least missing nonzero digit in the primorial base expansion of n.
6
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
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. A328840 (the positions of ones in this sequence).
Cf. A257079 for analogous sequence.
Sequence in context: A194326 A295277 A194290 * A257079 A327567 A260372
KEYWORD
nonn,base
AUTHOR
Antti Karttunen, Nov 03 2019
STATUS
approved