A069526 Smallest multiple of n with digit sum = 7, or 0 if no such number exists, e.g. a(3k)= a(11k) = 0.

7, 16, 0, 16, 25, 0, 7, 16, 0, 70, 0, 0, 52, 70, 0, 16, 34, 0, 133, 160, 0, 0, 115, 0, 25, 52, 0, 700, 232, 0, 124, 160, 0, 34, 70, 0, 0, 304, 0, 160, 205, 0, 43, 0, 0, 322, 1222, 0, 2401, 250, 0, 52, 106, 0, 0, 7000, 0, 232, 4012, 0, 61, 124, 0, 1024, 520, 0, 11122, 340

Offset: 1

Author

Amarnath Murthy, Apr 01 2002

Keywords

• nonn
• look
• base

Comments

Either no multiples of 37 have digit sum 7 or their first values are > 10000000. - Larry Reeves (larryr(AT)acm.org), Jul 02 2002

No multiples of 3, 11, 37, 101 or 271 have digit sum 7. - Robert Israel, Feb 13 2024

Links

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

Crossrefs

Cf. A052221, A069521, A069522, A069523, A069524, A069525, A069527, A069528.

Programs

Maple

unfinished:= true: V:= Vector(300): V0:= select(t -> igcd(t, 3*11*37*101*271) = 1, {$1..300}):
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
              v:= 10^i1 + 10^i2 + 10^i3 + 10^i4 + 10^i5 + 10^i6 + 10^i7;
              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:
convert(V,list); # Robert Israel, Feb 13 2024

Formula

a(n)= n*A088396(n). - R. J. Mathar, Aug 06 2019

Extensions

More terms from Larry Reeves, Jul 02 2002