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A172189 Numbers n with property that n reduced mod (sum of all the other digits) is d, for each digit d. 2
111, 199, 221, 222, 287, 331, 333, 375, 442, 444, 445, 485, 551, 554, 555, 557, 643, 662, 663, 666, 735, 739, 772, 775, 777, 827, 881, 884, 888, 919, 993, 999, 1011, 1101, 1111, 1121, 1144, 1276, 1333, 1414, 1453, 1771, 2022, 2177, 2202, 2222, 2225, 2242, 2288, 2355, 2531, 2532, 2537, 2666, 2828 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

COMMENTS

Suppose the decimal expansion of n is n = d(p)d(p-1)…d(0).

Then we require that n mod (s-d(k)) = d(k) for k=0..p.  [D. S. McNeil, Nov 21 2010; N. J. A. Sloane, Nov 20 2010]

LINKS

David A. Corneth, Table of n, a(n) for n = 1..10000

EXAMPLE

2537 is in the sequence because 2537 mod (5+3+7) = 2, 2537 mod (2+3+7) = 5, etc.

11 is not a member because 11 mod 1 is 0 not 1.

MAPLE

with(numtheory):T:=array(1..2000):for n from 1 to 3000 do:ind:=0: l:=length(n)

  : n0:=n:indic:=0:s:=0:p:=1:for m from 1 to l do: q:=n0:u:=irem(q, 10):v:=iquo(q, 10):n0:=v

  :s:=s+u: T[m]:=u:od:for i from 1 to l do:x:=T[i]: if (s-x) <>0 and irem(n, s-x)=x

  then ind:=ind+1:else fi:od:if ind=l then printf(`%d, `, n):else fi:od:

MATHEMATICA

Quiet@ Select[ Range[3000], (d = IntegerDigits@#; Mod[#, Total[d] - d] == d) &] (* Giovanni Resta, Mar 12 2019 *)

PROG

(PARI) isok(n) = {my(d = digits(n), s = vecsum(d)); for (k=1, #d, if (!(s-d[k]) || ((n % (s-d[k]) != d[k])), return(0)); ); 1; } \\ Michel Marcus, Mar 12 2019

CROSSREFS

Cf. A007953 (sum of digits).

Sequence in context: A074253 A245385 A245364 * A279777 A291797 A088287

Adjacent sequences:  A172186 A172187 A172188 * A172190 A172191 A172192

KEYWORD

nonn,base

AUTHOR

Michel Lagneau, Nov 20 2010

EXTENSIONS

Definition clarified by D. S. McNeil, Nov 20 2010

I rewrote the definition, comments and the example to take into account D. S. McNeil's clarifications. - N. J. A. Sloane, Nov 20 2010

STATUS

approved

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Last modified July 22 17:02 EDT 2019. Contains 325225 sequences. (Running on oeis4.)