A069529 Smallest multiple of n with digit sum = 10, or 0 if no such number exists, e.g. a(3k)= 0.

19, 28, 0, 28, 55, 0, 28, 64, 0, 190, 55, 0, 91, 28, 0, 64, 136, 0, 19, 280, 0, 154, 46, 0, 325, 208, 0, 28, 145, 0, 217, 64, 0, 136, 280, 0, 37, 190, 0, 280, 82, 0, 172, 352, 0, 46, 235, 0, 343, 550, 0, 208, 424, 0, 55, 280, 0, 406, 118, 0, 244, 1054, 0, 64, 325, 0, 1072

Offset: 1

Author

Amarnath Murthy, Apr 01 2002

Keywords

• base
• nonn

Comments

a(n) = 0 if n is a multiple of 3, 1111, 2849, 3367, 4649 or 5291.

Links

• Robert Israel, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A069521, A069522, A069523, A069524, A069525, A069526, A069527, A069528.

Programs

Maple

unfinished:= true: V:= Vector(1000):
V0:= select(t -> igcd(t, 3*4649) = 1 and t mod 1111 <> 0 and t mod 2849 <> 0 and t mod 3367 <> 0 and t mod 5291 <> 0, {$1..1000}):
for i1 from 0 while unfinished do
  for i2 from 0 to i1 while unfinished do
    for i3 from 0 to i2 while unfinished do
      for i4 from 0 to i3 while unfinished do
        for i5 from 0 to i4 while unfinished do
          for i6 from 0 to i5 while unfinished do
            for i7 from 0 to i6 while unfinished do
            for i8 from 0 to i7 while unfinished do
            for i9 from 0 to i8 while unfinished do
            for i10 from 0 to i9 while unfinished do
              v:= 10^i1 + 10^i2 + 10^i3 + 10^i4 + 10^i5 + 10^i6 + 10^i7 + 10^i8 + 10^i9 + 10^i10;
              if convert(convert(v,base,10),`+`) <> 10 then next fi;
              dv:= numtheory:-divisors(v);
              for s in V0 intersect dv do
                V[s]:= v;
              od;
              V0:= V0 minus dv;
              unfinished:= evalb(V0 <> {});
od od od od od od od od od od:
convert(V,list); # Robert Israel, Feb 14 2024

Extensions

More terms from Sascha Kurz, Apr 08 2002