A069528 Smallest multiple of n with digit sum = 9, or 0 if no such number exists (e.g., a(11k) = 0).

9, 18, 9, 36, 45, 18, 63, 72, 9, 90, 0, 36, 117, 126, 45, 144, 153, 18, 171, 180, 63, 0, 207, 72, 225, 234, 27, 252, 261, 90, 1116, 1152, 0, 306, 315, 36, 333, 342, 117, 360, 1107, 126, 1161, 0, 45, 414, 423, 144, 441, 450, 153, 1404, 1431, 54, 0, 504, 171, 522

Offset: 1

Author

Amarnath Murthy, Apr 01 2002

Keywords

• base
• nonn

Comments

a(n) = 0 if n is a multiple of 11, 101, 271, 999 or 4649. - Robert Israel, Feb 14 2024

Links

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

Crossrefs

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

Programs

Maple

unfinished:= true: V:= Vector(1000): V0:= select(t -> igcd(t, 11*101*271*4649) = 1 and t mod 999 <> 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
              v:= 10^i1 + 10^i2 + 10^i3 + 10^i4 + 10^i5 + 10^i6 + 10^i7 + 10^i8 + 10^i9;
              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:
convert(V,list); # Robert Israel, Feb 14 2024

Extensions

More terms from Sascha Kurz, Apr 08 2002