OFFSET
1,1
COMMENTS
The sequence is infinite if one considers numbers like 10........010 (with N zeros between ones, N = 0, 1, 2, ...). The problem of looking for odd terms and zerofree terms remains. Still unclear is whether the sequence contains infinitely many zerofree terms. The proportions between numbers of N-digit numbers included in the sequence need to be explored.
EXAMPLE
234 is divisible by 3*(2+4).
1020 is divisible by 2*(1+0).
1062 is divisible by 6*(1+2).
1250 is divisible by 25*(1+0).
MATHEMATICA
Select[Range[100, 2500], Mod[#1, If[#2 == 0, #1 - 1, #2] & @@ {#1, (First@ #2 + Last@ #2) FromDigits@ Most@ Rest@ #2}] == 0 & @@ {#, IntegerDigits@ #} &] (* Michael De Vlieger, Oct 11 2018 *)
PROG
(PARI) isok(n) = {d = digits(n); if (#d >= 3, x = d[1]; y = d[#d]; w = vector(#d-2, k, d[k+1]); z = fromdigits(w); if (z, return (!(n % (z*(x+y))))); ); return (0); } \\ Michel Marcus, Oct 07 2018
CROSSREFS
KEYWORD
nonn,base
AUTHOR
Anton Deynega, Oct 06 2018
STATUS
approved