A260385 Numbers such that n divides A260519(n), where A260519(n) is the concatenation of the positions of the digits 0, 1, ..., 9 in n, positions counted from the right, and 0 if a given digit does not occur.

1, 2, 4, 5, 10, 12, 15, 20, 24, 25, 30, 32, 40, 50, 56, 58, 59, 60, 69, 75, 100, 112, 120, 125, 150, 170, 175, 200, 220, 240, 250, 275, 276, 300, 320, 325, 366, 399, 400, 440, 500, 510, 525, 600, 660, 726, 775, 1000, 1250, 2000, 2200, 2360, 2413, 2500, 3142, 3200

Offset

1,2

Comments

A260274 is a subset of this sequence

Links

Paolo P. Lava, Table of n, a(n) for n = 1..160

Example

Consider number 56. We have no digit 0, 1, 2, 3 and 4, one digit 5 in position 2, one digit 6 in position 1 and no digit 7, 8 and 9. Therefore we get 0000021000 and 21000 / 56 = 375.
Consider 774452318582. We have no digit 0, one digit 1 in position 5, two digits 2 in position 1 and 7, one digit 3 in position 6, two digits 4 in position 9 and 10, two digits 5 in position 3 and 8, no digit 6, two digits 7 in position 11 and 12, two digits 8 in position 2 and 4 and no digit 9. Therefore 774452318582 is transformed in 51769103801112240. But 51769103801112240 / 774452318582 = 66846.08278... 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 0 to 9 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, A260519(n)%n||print1(n", ")) \\ M. F. Hasler, Jul 28 2015

Crossrefs

Cf. A260274, A260275, A260386, A260519-A260522.

Sequence in context: A325095 A120491 A177186 * A355149 A022944 A370593

Adjacent sequences: A260382 A260383 A260384 * A260386 A260387 A260388

Keyword

nonn,base

Author

Paolo P. Lava, Jul 24 2015

Status

approved