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Minimum number k for which the digital sum of k*n is 10*n.
2

%I #13 Mar 21 2016 03:13:52

%S 0,19,199,1333,17497,199999,1333333,12842857,374999986,1111111111,

%T 199999999999,1090909090909,4999999999999,46076923076923,

%U 571427857142857,13333333333333333,124999999999999993,588235235294117647,11111111111111111111,157894731578947368421

%N Minimum number k for which the digital sum of k*n is 10*n.

%p P:=proc(i) local j,k,n,ok,w; for n from 0 by 1 to i do j:=-1; ok:=1; while ok=1 do j:=j+1; w:=0; k:=n*j; while k>0 do w:=w+k-(trunc(k/10)*10); k:=trunc(k/10); od; if w=10*n then ok:=0; print(j); fi; od; od; end: P(100);

%o (PARI) a(n) = {my(k = 0); while (sumdigits(k*n) != 10*n, k++); k;}; \\ _Michel Marcus_, Mar 21 2016

%Y Cf. A147822-A147829, A147831.

%K easy,nonn,base

%O 0,2

%A _Paolo P. Lava_ and _Giorgio Balzarotti_, Nov 14 2008

%E Edited by _Charles R Greathouse IV_, Nov 01 2009

%E a(6)-a(10) from _Donovan Johnson_, Sep 16 2012

%E a(11)-a(19) from _Chai Wah Wu_, Mar 20 2016