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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. 5
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 (list; graph; refs; listen; history; text; internal format)
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: A063465 A287346 A035001 * A092268 A335702 A069259

Adjacent sequences:  A260383 A260384 A260385 * A260387 A260388 A260389

KEYWORD

nonn,base

AUTHOR

Paolo P. Lava, Jul 24 2015

STATUS

approved

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Last modified May 17 15:35 EDT 2021. Contains 343980 sequences. (Running on oeis4.)