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

0, 2, 4, 6, 4, 15, 12, 14, 16, 18, 30, 33, 12, 39, 42, 45, 16, 51, 18, 38, 40, 42, 22, 92, 24, 50, 52, 54, 28, 87, 60, 62, 64, 66, 102, 105, 72, 74, 76, 78, 120, 123, 126, 129, 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

Offset: 0

Author

Antti Karttunen, Apr 27 2022

Keywords

• nonn
• base

Examples

			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.
		

Links

• Amiram Eldar, Table of n, a(n) for n = 0..10000
• Index entries for sequences related to primorial base.

Crossrefs

Cf. A049345, A328840 (the fixed points, positions where a(n) = n), A329028.

Cf. also A257080 for analogous sequence.

Programs

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]]; n * Min[Complement[Range[Max[s]+1], s]]]; a[0] = 0; Array[a, 100, 0] (* Amiram Eldar, Mar 13 2024 *)

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))); };
A353512(n) = (n * A329028(n));

Formula

a(n) = n * A329028(n).