A069521 Smallest multiple of n with digit sum = 2, or 0 if no such number exists, e.g., a(3k)=0.

2, 2, 0, 20, 20, 0, 1001, 200, 0, 20, 11, 0, 1001, 10010, 0, 2000, 100000001, 0, 1000000001, 20, 0, 110, 100000000001, 0, 200, 10010, 0, 100100, 100000000000001, 0, 0, 20000, 0, 1000000010, 10010, 0, 0, 10000000010, 0, 200, 0, 0, 0, 1100, 0

Offset

1,1

Comments

a(n)=0 if n is a multiple of 3, 31, 37, 41, 43, 53, 67, 71, 79, or 83. - Ray Chandler, Jul 30 2003

Links

Robert Israel, Table of n, a(n) for n = 1..2016

Formula

From Robert Israel, Feb 11 2023: (Start)

If n = 2^a * 5^b, a(n) = 2*10^max(a-1,b).

Otherwise, if n = 2^a*5^b*c where c is in A043292, then a(n) = 10^max(a,b) * (1 + 10^A069531(c)).

Otherwise a(n) = 0. (End)

Example

a(7) = a(13) = 1001. Digit sum of 1001 = 2 and is the smallest such multiple of 7 and 13. a(17) = 100000001 = 17*5882353.

Maple

f:= proc(n) local a, b, c, k;
  a:= padic:-ordp(n, 2);
  b:= padic:-ordp(n, 5);
  c:= n/(2^a*5^b);
  if c = 1 then return 2*10^max(a-1, b) fi;
  k:= traperror(NumberTheory:-ModularLog(-1, 10, c));
  if k = "no solutions exist" then 0
  else 10^max(a, b) * (1 + 10^k)
  fi
end proc:
map(f, [$1..50]); # Robert Israel, Feb 11 2023

Crossrefs

Cf. A043292, A069531.

Sequence in context: A134085 A151339 A228273 * A245687 A228617 A119836

Adjacent sequences: A069518 A069519 A069520 * A069522 A069523 A069524

Keyword

base,nonn

Author

Amarnath Murthy, Apr 01 2002

Extensions

More terms from Ray Chandler, Jul 30 2003

Status

approved