A260348 Numbers n such that n is divisible by (10^k - digitsum(n)), where k equals the number of digits of digitsum(n).

5, 8, 9, 18, 21, 24, 26, 27, 36, 44, 45, 50, 54, 60, 62, 63, 72, 80, 81, 86, 90, 108, 116, 117, 126, 132, 134, 135, 140, 144, 152, 153, 162, 170, 171, 180, 200, 204, 206, 207, 210, 216, 224, 225, 230, 234, 240, 242, 243, 252, 260, 261, 264, 270, 306, 312, 314

Offset

1,1

Comments

This sequence is infinite because all numbers with a digitsum equal to 9 are part of this sequence.

Links

Pieter Post, Table of n, a(n) for n = 1..12089

Example

a(1) = 5, because 5 divided by (10 - 5) equals 1.
a(7) = 26, because digitsum(26) = 8 and 26 divided by (10 - 8) equals 13.
a(20) = 86, the first member of this sequence where digitsum(n) >= 10. Digitsum(86) = 14, so k = 10^2 - 14 = 86, so 86 is a member of this sequence.

Mathematica

fQ[n_] := Block[{d = Total@ IntegerDigits@ n, k}, k = IntegerLength@ d;
  Divisible[n, 10^k - d]]; Select[Range@ 314, fQ] (* or *)
Select[Range@ 314, Divisible[#, (10^(Floor[Log[10, Total@ IntegerDigits@ #]] + 1) - Total@ IntegerDigits@ #)] &] (* Michael De Vlieger, Aug 05 2015 *)

Prog

(Python)
def sod(n, m):
....kk = 0
....while n > 0:
........kk= kk+(n%m)
........n =int(n//m)
....return kk
for c in range (1, 10**6):
....k=len(str(sod(c, 10)))
....kl=10**k-sod(c, 10)
....if c%kl==0:
........print (c)
(PARI) isok(n)=my(sd = sumdigits(n), nsd = #digits(sd)); n % (10^nsd - sd) == 0; \\ Michel Marcus, Aug 05 2015

Crossrefs

Cf. A005349, A007953, A113315.

Sequence in context: A046287 A051220 A102785 * A276934 A127493 A331442

Adjacent sequences: A260345 A260346 A260347 * A260349 A260350 A260351

Keyword

nonn,base,less

Author

Pieter Post, Jul 23 2015

Status

approved