A365375 Numbers being the smallest positive integer having its digits (Cf. A179239) from which two digits can be chosen, the difference being any value from 0 to 9.

100269, 100479, 101269, 101479, 102269, 102669, 102699, 104479, 104779, 104799, 200589, 202589, 205589, 205889, 205899, 300789, 303789, 307789, 307889, 307899, 1000269, 1000479, 1001269, 1001479, 1002269, 1002349, 1002359, 1002369, 1002379, 1002469, 1002479, 1002489, 1002569, 1002579

Offset: 1

Author

Eric Angelini and Giorgos Kalogeropoulos, Sep 02 2023

Keywords

• base
• nonn

Comments

Anagrams of the terms are not included in the sequence.

There are 320 such numbers up to 10^7, the largest being 5067899.

Examples

			a(1) = 100269 and we have:
  0 = 0 - 0
  1 = 1 - 0
  2 = 2 - 0
  3 = 9 - 6
  4 = 6 - 2
  5 = 6 - 1
  6 = 6 - 0
  7 = 9 - 2
  8 = 9 - 1
  9 = 9 - 0
The integer 102069 being an anagram of 100269 is not in the sequence (though 102069 also produces the 10 digits).
		

Links

• David A. Corneth, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A179239, A219248.

Programs

Mathematica

lst={};Do[If[Union@Flatten[Abs@*Differences/@Subsets[IntegerDigits@k,{2}]]==Range[0,9],If[FreeQ[lst,s=Sort@IntegerDigits@k],AppendTo[lst,s];Print@k]],{k,10^6}]

Python

from itertools import count, islice, combinations, combinations_with_replacement as mc
def c(t):
    d = list(map(int, t))
    return len(set(abs(d[i]-d[j]) for i, j in combinations(range(len(d)), 2))) == 10
def bgen():
    D = "123456789"
    return ((D[i],)+r for d in count(1) for i in range(9) for r in mc("0"+D[i:], d-1))
def agen():
    yield from (int("".join(t)) for t in filter(c, bgen()))
print(list(islice(agen(), 34))) # Michael S. Branicky, Sep 11 2024

Extensions

Name specified by David A. Corneth, Sep 11 2024