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

1,1

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.

Links

Table of n, a(n) for n=1..12.

Example

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

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)]);

Prog

(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
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

Crossrefs

Cf. A297330.

Sequence in context: A254770 A254777 A254723 * A031631 A250923 A015630

Adjacent sequences: A354209 A354210 A354211 * A354213 A354214 A354215

Keyword

nonn,base,more

Author

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

Status

approved