A350444 a(n) is the smallest number that has not appeared yet in the sequence and has only one digit in common with a(n-1).

1, 10, 12, 2, 20, 21, 13, 3, 23, 24, 4, 14, 15, 5, 25, 26, 6, 16, 17, 7, 27, 28, 8, 18, 19, 9, 29, 32, 30, 31, 34, 35, 36, 37, 38, 39, 43, 40, 41, 42, 45, 46, 47, 48, 49, 54, 50, 51, 52, 53, 56, 57, 58, 59, 65, 60, 61, 62, 63, 64, 67, 68, 69, 76, 70, 71, 72, 73, 74, 75, 78, 79, 87, 80, 81, 82, 83, 84, 85, 86, 89, 90

Offset: 1

Author

Rodolfo Kurchan, Dec 31 2021

Keywords

• nonn
• base

Comments

Terms computed by Claudio Meller.

It appears that this sequence contains all numbers except those in A115853.

Examples

			a(2) = 10 because it is the smallest number that has exactly one digit in common with a(1) = 1; similarly, a(3) = 12 because it has one digit in common with a(2) = 10 and a(4) = 2 because it is the smallest number that is not already in the sequence that has exactly one digit in common with a(3) = 12.
		

Links

• Michael De Vlieger, Log-log scatterplot of a(n) for n = 1..10000 labeling the first 40 terms.

Crossrefs

Cf. A115853, A350445.

Programs

Mathematica

c[] = False; j = c[1] = 1; {j}~Join~Reap[Do[d = Union@ IntegerDigits[j]; If[j == u, While[c[u] > 0, u++]]; k = u; While[Nand[c[k] == False, Count[IntegerDigits[k], ?(MemberQ[d, #] &)] == 1], k++]; Sow[k]; c[k] = True; j = k, 81]][[-1, -1]] (* Michael De Vlieger, Dec 31 2021 *)

Python

from itertools import islice
def c(s, t): return sum(t.count(si) for si in s)
def agen(): # generator of terms
    an, target, seen, mink = 1, "1", {1}, 2
    while True:
        yield an
        k = mink
        while k in seen or c(str(k), target) != 1: k += 1
        an, target = k, str(k)
        seen.add(an)
        while mink in seen: mink += 1
print(list(islice(agen(), 82))) # Michael S. Branicky, Dec 31 2021