A260386 Numbers n which divide A260521(n), the concatenation of the positions of the digits 9, 8, ..., 0 in the decimal representation of n, where positions are counted from the right, and 0 if a given digit does not occur.

1, 2, 4, 5, 8, 12, 15, 19, 21, 24, 25, 48, 68, 75, 96, 123, 228, 231, 275, 312, 321, 375, 451, 484, 712, 726, 768, 868, 1234, 1324, 2143, 2341, 3412, 3421, 4123, 4231, 4312, 4321, 4544, 11425, 12345, 13425, 14235, 14325, 21354, 23451, 24153, 24351, 31524, 32541

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

A260275 is a subset of this sequence.

Cf. A260274, A260275, A260385, A260519-A260522.

Sequence in context: A287346 A344841 A035001 * A092268 A335702 A069259

Adjacent sequences: A260383 A260384 A260385 * A260387 A260388 A260389

Keyword

nonn,base

Author

Paolo P. Lava, Jul 24 2015

Status

approved