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A354212 Numbers k such that A297330(k)*k and k have the same digits but in a different order.

%I A354212 #18 May 31 2022 11:02:10
%S A354212 11688,116688,126888,1166688,1266888,11666688,12446778,12666888,
%T A354212 116666688,123456789,124466778,126666888
%N A354212 Numbers k such that A297330(k)*k and k have the same digits but in a different order.
%C A354212 Contains all numbers of the forms 116...688, 12446...6778, and 126...6888 (with at least one 6).
%C A354212 All terms are divisible by 3.
%e A354212 a(1) = 11688 is a term because A297330(11688) = 7 and 7*11688 = 81816 has the same digits as 11688 in a different order.
%p A354212 filter:= proc(n) local L,m;
%p A354212   L:= convert(n,base,10);
%p A354212   m:= convert(map(abs,L[2..-1]-L[1..-2]),`+`);
%p A354212   if m = 1 then return false fi;
%p A354212   sort(L) = sort(convert(m*n,base,10))
%p A354212 end proc:
%p A354212 select(filter, [seq(i,i=3..10^7,3)]);
%o A354212 (PARI) f(n) = my(d=digits(n)); sum(i=2, #d, if (d[i]<d[i-1], d[i-1]-d[i])) + sum(i=2, #d, if (d[i]>d[i-1], d[i]-d[i-1])); \\ A297330
%o A354212 isok(k) = my(d=digits(k), dd = digits(k*f(k))); (d != dd) && vecsort(d) == vecsort(dd); \\ _Michel Marcus_, May 19 2022
%o A354212 (Python)
%o A354212 from itertools import count, islice
%o A354212 def A354212_gen(startvalue=1): # generator of terms >= startvalue
%o A354212     for n in count(max(startvalue,1)):
%o A354212         s = str(n)
%o A354212         t = str(n*sum(abs(int(s[i])-int(s[i+1])) for i in range(len(s)-1)))
%o A354212         if s != t and sorted(s) == sorted(t):
%o A354212             yield n
%o A354212 A354212_list = list(islice(A354212_gen(),5)) # _Chai Wah Wu_, May 31 2022
%Y A354212 Cf. A297330.
%K A354212 nonn,base,more
%O A354212 1,1
%A A354212 _J. M. Bergot_ and _Robert Israel_, May 19 2022