A383789 a(1) = 1; for n > 1, a(n) is the smallest positive integer not already in the sequence such that it shares at least one digit with a(n-1), and it has a different number of digits from a(n-1).

1, 10, 100, 11, 101, 12, 2, 20, 102, 13, 3, 23, 103, 14, 4, 24, 104, 15, 5, 25, 105, 16, 6, 26, 106, 17, 7, 27, 107, 18, 8, 28, 108, 19, 9, 29, 109, 21, 110, 30, 113, 31, 111, 41, 112, 22, 120, 32, 121, 42, 114, 34, 123, 33, 130, 35, 115, 45, 124, 40, 134, 36, 116, 46, 126, 51, 117, 37, 127, 47, 137

Offset: 1

Author

Ali Sada, May 09 2025

Keywords

• nonn
• base

Examples

			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.
		

Links

• Vincenzo Librandi, Table of n, a(n) for n = 1..1000

Crossrefs

Cf. A184992, A303848.

Programs

Magma

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

Mathematica

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 *)

PARI

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