OFFSET
1,2
COMMENTS
Given a number n with k digits, label the positions of the digits starting from LSD = 1 to MSD = k. Then concatenate in ascending order the positions of digit 9 in n. Repeat the same process for digits from 8 down to 0. If a digit is not present in n put 0. Sequence lists the numbers that under this transform produce a multiple of the number itself.
LINKS
Paolo P. Lava, Table of n, a(n) for n = 1..500
EXAMPLE
Consider number 75. We have no digit 9 and 8, one digit 7 in position 2, no digit 6, one digit 5 in position 1, no digit 4, 3, 2, 1 and 0. Therefore we get 002100000 and 2100000 / 75 = 28000.
Consider 774452318582. We have no digit 9, two digits 8 in positions 2 and 4, two digits 7 in positions 11 and 12, no digit 6, two digit 5 in positions 3 and 8, two digits 4 in positions 9 and 10, one digit 3 in position 6, two digits 2 in positions 1 and 7, one digit 1 in position 5 and no digit 0. Therefore 774452318582 is transformed in 024111203891061750. But 24111203891061750 / 774452318582 = 31133.2322... Therefore 774452318582 is not part of the sequence.
MAPLE
with(numtheory): P:=proc(q) local a, b, j, k, ok, n;
for n from 1 to q do a:=convert(n, base, 10); b:=0;
for k from 9 by -1 to 0 do ok:=0; for j from 1 to nops(a) do
if a[j]=k then ok:=1; b:=b*10^(ilog10(j)+1)+j; fi; od;
if ok=0 then b:=10*b; fi; od; if type(b/n, integer) then print(n);
fi; od; end: P(10^9);
PROG
(PARI) for(n=1, 9e9, A260521(n)%n||print1(n", ")) \\ M. F. Hasler, Jul 28 2015
CROSSREFS
KEYWORD
nonn,base
AUTHOR
Paolo P. Lava, Jul 24 2015
STATUS
approved