A131382 Minimal number m such that Sum_digits(n*m)=n.

1, 1, 1, 1, 1, 1, 1, 1, 1, 19, 19, 4, 19, 19, 13, 28, 28, 11, 46, 199, 19, 109, 73, 37, 199, 73, 37, 271, 172, 1333, 289, 559, 1303, 847, 1657, 833, 1027, 1576, 1282, 17497, 4339, 2119, 2323, 10909, 11111, 12826, 14617, 14581, 16102, 199999, 17449, 38269

Offset: 1

Author

Paolo P. Lava and Giorgio Balzarotti, Jul 09 2007

Keywords

• base
• nonn

Examples

			n=23 --> a=73 because 23*73 = 1679 and 1+6+7+9=23.
n=34 --> a=847 because 34*847 = 28798 and 2+8+7+9+8=34.
		

Links

• Peter Lomax, Table of n, a(n) for n = 1..1000 (first 90 terms from T. D. Noe)
• H. Fredricksen, E. J. Ionascu, F. Luca, and P. Stanica, Minimal Niven numbers, arXiv:0803.0477 [math.NT], 2008.
• Peter Lomax, Phix program for generating 1000 terms

Crossrefs

Cf. A005349, A002998.

Programs

Maple

P:=proc(n) local i,j,k,w; for i from 1 by 1 to n do for j from 1 to n do w:=0; k:=i*j; while k>0 do w:=w+k-(trunc(k/10)*10); k:=trunc(k/10); od; if i=w then print(j); break; fi; od; od; end: P(1000000);

Mathematica

m[n_]:=Module[{m=1},While[Total[IntegerDigits[m*n]]!=n,m++];m]; Array[m,60] (* Harvey P. Dale, Sep 28 2013 *)

PARI

a(n)=my(k);while(sumdigits(k+=n)!=n,); k/n \\ Charles R Greathouse IV, Feb 01 2013

Formula

a(n) = A002998(n) / n. - Michel Marcus, Dec 10 2012