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

Author

Pieter Post, Jul 23 2015

Keywords

• nonn
• base
• less

Comments

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

Examples

			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.
		

Links

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

Crossrefs

Cf. A005349, A007953, A113315.

Programs

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 *)

PARI

isok(n)=my(sd = sumdigits(n), nsd = #digits(sd)); n % (10^nsd - sd) == 0; \\ Michel Marcus, Aug 05 2015

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)