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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.

%I A365375 #27 Jun 16 2025 23:49:01
%S A365375 100269,100479,101269,101479,102269,102669,102699,104479,104779,
%T A365375 104799,200589,202589,205589,205889,205899,300789,303789,307789,
%U A365375 307889,307899,1000269,1000479,1001269,1001479,1002269,1002349,1002359,1002369,1002379,1002469,1002479,1002489,1002569,1002579
%N 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.
%C A365375 Anagrams of the terms are not included in the sequence.
%C A365375 There are 320 such numbers up to 10^7, the largest being 5067899.
%H A365375 David A. Corneth, <a href="/A365375/b365375.txt">Table of n, a(n) for n = 1..10000</a>
%e A365375 a(1) = 100269 and we have:
%e A365375   0 = 0 - 0
%e A365375   1 = 1 - 0
%e A365375   2 = 2 - 0
%e A365375   3 = 9 - 6
%e A365375   4 = 6 - 2
%e A365375   5 = 6 - 1
%e A365375   6 = 6 - 0
%e A365375   7 = 9 - 2
%e A365375   8 = 9 - 1
%e A365375   9 = 9 - 0
%e A365375 The integer 102069 being an anagram of 100269 is not in the sequence (though 102069 also produces the 10 digits).
%t A365375 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}]
%o A365375 (Python)
%o A365375 from itertools import count, islice, combinations, combinations_with_replacement as mc
%o A365375 def c(t):
%o A365375     d = list(map(int, t))
%o A365375     return len(set(abs(d[i]-d[j]) for i, j in combinations(range(len(d)), 2))) == 10
%o A365375 def bgen():
%o A365375     D = "123456789"
%o A365375     return ((D[i],)+r for d in count(1) for i in range(9) for r in mc("0"+D[i:], d-1))
%o A365375 def agen():
%o A365375     yield from (int("".join(t)) for t in filter(c, bgen()))
%o A365375 print(list(islice(agen(), 34))) # _Michael S. Branicky_, Sep 11 2024
%Y A365375 Cf. A179239, A219248.
%K A365375 base,nonn
%O A365375 1,1
%A A365375 _Eric Angelini_ and _Giorgos Kalogeropoulos_, Sep 02 2023
%E A365375 Name specified by _David A. Corneth_, Sep 11 2024