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

11688, 116688, 126888, 1166688, 1266888, 11666688, 12446778, 12666888, 116666688, 123456789, 124466778, 126666888

Offset: 1

Author

J. M. Bergot and Robert Israel, May 19 2022

Keywords

• nonn
• base
• more

Comments

Contains all numbers of the forms 116...688, 12446...6778, and 126...6888 (with at least one 6).

All terms are divisible by 3.

Examples

			a(1) = 11688 is a term because A297330(11688) = 7 and 7*11688 = 81816 has the same digits as 11688 in a different order.
		

Crossrefs

Cf. A297330.

Programs

Maple

filter:= proc(n) local L,m;
  L:= convert(n,base,10);
  m:= convert(map(abs,L[2..-1]-L[1..-2]),`+`);
  if m = 1 then return false fi;
  sort(L) = sort(convert(m*n,base,10))
end proc:
select(filter, [seq(i,i=3..10^7,3)]);

PARI

f(n) = my(d=digits(n)); sum(i=2, #d, if (d[i]d[i-1], d[i]-d[i-1])); \\ A297330
isok(k) = my(d=digits(k), dd = digits(k*f(k))); (d != dd) && vecsort(d) == vecsort(dd); \\ Michel Marcus, May 19 2022

Python

from itertools import count, islice
def A354212_gen(startvalue=1): # generator of terms >= startvalue
    for n in count(max(startvalue,1)):
        s = str(n)
        t = str(n*sum(abs(int(s[i])-int(s[i+1])) for i in range(len(s)-1)))
        if s != t and sorted(s) == sorted(t):
            yield n
A354212_list = list(islice(A354212_gen(),5)) # Chai Wah Wu, May 31 2022