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.
%I A384597 #9 Jun 16 2025 21:50:47
%S A384597 1,41,73,631,793,6031,6391,6733,7412,7520,7993,8627,9710,25147,37112,
%T A384597 43916,49316,51427,60031,60391,60733,62314,63214,63991,66331,67393,
%U A384597 67933,70211,71132,72101,74102,74912,75020,75290,78260,79993,81103,85712,86927,89627
%N A384597 Integers k such that k + 1 has a divisor that is an anagram of k, which must have the same number of digits as k.
%C A384597 This sequence has infinitely many terms, since 60*10^m + 31 is a term for all positive integers m, as (60*10^m + 31) + 1 = 2*(30*10^m + 16).
%C A384597 A100412 is a subsequence of a(n), since if m is in A100412, then m + 1 = 2*reversal(m).
%e A384597 73 is in this sequence since 73 + 1 = 37*2, where 37 is an anagram of 73.
%t A384597 {1}~Join~Select[Range[100000],ContainsAny[IntegerDigits/@Divisors[#+1],Complement[Permutations[IntegerDigits[#]],{IntegerDigits[#]}]]&] (* _James C. McMahon_, Jun 10 2025 *)
%o A384597 (Python)
%o A384597 def ok(k):
%o A384597 return any((k+1)%d==0 and sorted(str(d))==sorted(str(k)) and len(str(d))==len(str(k)) for d in range(1,k+2))
%o A384597 print(", ".join(map(str, [k for k in range(1, 100000) if ok(k)])))
%o A384597 (PARI) isok(k) = my(s=vecsort(digits(k))); fordiv(k+1, d, if (vecsort(digits(d)) == s, return(1))); \\ _Michel Marcus_, Jun 04 2025
%Y A384597 Cf. A100412.
%K A384597 nonn,base
%O A384597 1,2
%A A384597 _Gonzalo MartÃnez_, Jun 04 2025