A043292 -id:A043292 - cp's OEIS frontend

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

Amarnath Murthy, Apr 01 2002

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

			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.

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

Cf. A043292, A069531.

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

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)

More terms from Ray Chandler, Jul 30 2003

A346991 Numbers occurring as divisors of 2^k + 5^k, k > 0.

Original entry on oeis.org

1, 7, 11, 17, 19, 23, 29, 37, 41, 47, 49, 53, 59, 61, 73, 77, 89, 97, 101, 103, 109, 113, 121, 127, 131, 133, 137, 139, 149, 161, 167, 173, 179, 181, 193, 209, 211, 223, 229, 233, 241, 251, 253, 257, 259, 263, 269, 277, 281, 287, 289, 313, 317, 329, 331, 337, 343

Offset: 1

Hugo Pfoertner, Aug 11 2021

nonn

If k is a term, then so are all divisors of k. - Robert Israel, Dec 08 2022

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

Cf. A074600, A043292.

filter:= proc(n) local q, v;
   if igcd(n,10) <> 1 then return false fi;
   q:= 5/2 mod n;
   traperror(NumberTheory:-ModularLog(-1,q,n)) <> lasterror
end proc:
filter(1):= true:
select(filter, [$1..400]); # Robert Israel, Dec 08 2022

cp's OEIS Frontend

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

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