This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
a(6) = 12, and 2 is the smallest number not already in the sequence that shares a digit with 12 and has a different number of digits. So, a(7) = 2.
function MySequence(N) a := [1]; while #a lt N do prev := a[#a]; d := Intseq(prev); m := #d; k := 2; repeat is_used := k in a; inter := &and[not x in d : x in Intseq(k)]; len_eq := #Intseq(k) eq m; k +:= 1; until not is_used and not inter and not len_eq; Append(~a, k - 1); end while; return a; end function; MySequence(100); // Vincenzo Librandi, May 17 2025
a[1] = 1; a[n_] := a[n] = Module[{k = 2, s = Array[a, n-1], d = IntegerDigits[a[n-1]], m = IntegerLength[a[n-1]]}, While[! FreeQ[s, k] || Intersection[IntegerDigits[k], d] == {} || IntegerLength[k] == m, k++]; k]; Array[a, 100] (* Amiram Eldar, May 10 2025 *)
isok(k, nbd, s, va) = if (#select(x->(x==k), va), return(0)); my(d=digits(k)); if (#setintersect(Set(d), s) && (#d != nbd), return(1)); find(va, n) = my(k=2, d=digits(va[n-1]), nbd=#d, s=Set(d)); while (!isok(k, nbd, s, va), k++); k; lista(nn) = my(va = vector(nn)); va[1] = 1; for (n=2, nn, va[n] = find(va, n);); va; \\ Michel Marcus, May 13 2025