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A353512 n multiplied by the least nonzero digit missing from its primorial base representation.

%I A353512 #12 Mar 13 2024 01:50:53
%S A353512 0,2,4,6,4,15,12,14,16,18,30,33,12,39,42,45,16,51,18,38,40,42,22,92,
%T A353512 24,50,52,54,28,87,60,62,64,66,102,105,72,74,76,78,120,123,126,129,
%U A353512 132,135,138,141,96,98,100,102,208,212,108,110,112,114,174,177,60,183,186,189,64,195,198,201,204,207,210,213,72
%N A353512 n multiplied by the least nonzero digit missing from its primorial base representation.
%H A353512 Amiram Eldar, <a href="/A353512/b353512.txt">Table of n, a(n) for n = 0..10000</a>
%H A353512 <a href="/index/Pri#primorialbase">Index entries for sequences related to primorial base</a>.
%F A353512 a(n) = n * A329028(n).
%e A353512 19 in primorial base (A049345) is written as "301". The least missing nonzero digit is 2, thus A329028(19) = 2 and a(19) = 2*19 = 38.
%t A353512 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]]; n * Min[Complement[Range[Max[s]+1], s]]]; a[0] = 0; Array[a, 100, 0] (* _Amiram Eldar_, Mar 13 2024 *)
%o A353512 (PARI)
%o A353512 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))); };
%o A353512 A353512(n) = (n * A329028(n));
%Y A353512 Cf. A049345, A328840 (the fixed points, positions where a(n) = n), A329028.
%Y A353512 Cf. also A257080 for analogous sequence.
%K A353512 nonn,base
%O A353512 0,2
%A A353512 _Antti Karttunen_, Apr 27 2022