cp's OEIS Frontend

A069527 Smallest multiple of n with digit sum = 8, or 0 if no such number exists, e.g. a(3k)= 0.

%I A069527 #14 Feb 15 2024 01:14:11
%S A069527 8,8,0,8,35,0,35,8,0,80,44,0,26,224,0,80,17,0,152,80,0,44,161,0,125,
%T A069527 26,0,224,116,0,62,224,0,170,35,0,0,152,0,80,1025,0,215,44,0,1610,611,
%U A069527 0,1421,350,0,260,53,0,440,224,0,116,413,0,305,62,0,512,260,0,134,1700,0
%N A069527 Smallest multiple of n with digit sum = 8, or 0 if no such number exists, e.g. a(3k)= 0.
%C A069527 The number ABCDEF (A through F are digits) is divisible by 37 if the number XYZ (where X=A+D, Y=B+E, Z=C+F) is divisible by 37. If the digit sum of XYZ is S, then the digit sum of ABCDEF is S+9k for some k. A quick check of all multiples of 37 with three or fewer digits shows that none have a digit sum of 8. Thus no multiple of 37 has a digit sum of 8 and a(37) is undefined as is a(37p) for all p. - Christopher Lund (clund(AT)san.rr.com), Apr 16 2002
%C A069527 a(n) = 0 if n is a multiple of 3, 37, 271 or 4649. - _Robert Israel_, Feb 14 2024
%H A069527 Robert Israel, <a href="/A069527/b069527.txt">Table of n, a(n) for n = 1..10000</a>
%F A069527 a(n) = n*A088397(n).
%p A069527 unfinished:= true: V:= Vector(1000): V0:= select(t -> igcd(t, 3*37*271*4649) = 1, {$1..1000}):
%p A069527 for i1 from 0 while unfinished do
%p A069527   for i2 from 0 to i1 while unfinished do
%p A069527     for i3 from 0 to i2 while unfinished do
%p A069527       for i4 from 0 to i3 while unfinished do
%p A069527         for i5 from 0 to i4 while unfinished do
%p A069527           for i6 from 0 to i5 while unfinished do
%p A069527             for i7 from 0 to i6 while unfinished do
%p A069527               for i8 from 0 to i7 while unfinished do
%p A069527               v:= 10^i1 + 10^i2 + 10^i3 + 10^i4 + 10^i5 + 10^i6 + 10^i7 + 10^i8;
%p A069527               dv:= numtheory:-divisors(v);
%p A069527               for s in V0 intersect dv do
%p A069527                 V[s]:= v;
%p A069527               od;
%p A069527               V0:= V0 minus dv;
%p A069527               unfinished:= evalb(V0 <> {});
%p A069527 od od od od od od od od:
%p A069527 convert(V,list); # _Robert Israel_, Feb 14 2024
%Y A069527 Cf. A069521, A069522, A069523, A069524, A069525, A069526.
%K A069527 base,nonn
%O A069527 1,1
%A A069527 _Amarnath Murthy_, Apr 01 2002
%E A069527 More terms from Christopher Lund (clund(AT)san.rr.com), Apr 16 2002