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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).

%I A260348 #36 May 22 2025 10:21:43
%S A260348 5,8,9,18,21,24,26,27,36,44,45,50,54,60,62,63,72,80,81,86,90,108,116,
%T A260348 117,126,132,134,135,140,144,152,153,162,170,171,180,200,204,206,207,
%U A260348 210,216,224,225,230,234,240,242,243,252,260,261,264,270,306,312,314
%N A260348 Numbers n such that n is divisible by (10^k - digitsum(n)), where k equals the number of digits of digitsum(n).
%C A260348 This sequence is infinite because all numbers with a digitsum equal to 9 are part of this sequence.
%H A260348 Pieter Post, <a href="/A260348/b260348.txt">Table of n, a(n) for n = 1..12089</a>
%e A260348 a(1) = 5, because 5 divided by (10 - 5) equals 1.
%e A260348 a(7) = 26, because digitsum(26) = 8 and 26 divided by (10 - 8) equals 13.
%e A260348 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.
%t A260348 fQ[n_] := Block[{d = Total@ IntegerDigits@ n, k}, k = IntegerLength@ d;
%t A260348   Divisible[n, 10^k - d]]; Select[Range@ 314, fQ] (* or *)
%t A260348 Select[Range@ 314, Divisible[#, (10^(Floor[Log[10, Total@ IntegerDigits@ #]] + 1) - Total@ IntegerDigits@ #)] &] (* _Michael De Vlieger_, Aug 05 2015 *)
%o A260348 (Python)
%o A260348 def sod(n,m):
%o A260348     kk = 0
%o A260348     while n > 0:
%o A260348         kk= kk+(n%m)
%o A260348         n =int(n//m)
%o A260348     return kk
%o A260348 for c in range (1, 10**6):
%o A260348     k=len(str(sod(c,10)))
%o A260348     kl=10**k-sod(c,10)
%o A260348     if c%kl==0:
%o A260348         print (c)
%o A260348 (PARI) isok(n)=my(sd = sumdigits(n), nsd = #digits(sd)); n % (10^nsd - sd) == 0; \\ _Michel Marcus_, Aug 05 2015
%Y A260348 Cf. A005349, A007953, A113315.
%K A260348 nonn,base,less
%O A260348 1,1
%A A260348 _Pieter Post_, Jul 23 2015