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A260348 Numbers n such that n is divisible by (10^k - digitsum(n)), where k equals the number of digits of digitsum(n). 1
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 (list; graph; refs; listen; history; text; internal format)
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 A006186

Adjacent sequences:  A260345 A260346 A260347 * A260349 A260350 A260351

KEYWORD

nonn,base,less

AUTHOR

Pieter Post, Jul 23 2015

STATUS

approved

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Last modified October 14 15:03 EDT 2019. Contains 328019 sequences. (Running on oeis4.)