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A069521 Smallest multiple of n with digit sum = 2, or 0 if no such number exists, e.g., a(3k)=0. 22
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 (list; graph; refs; listen; history; text; internal format)
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

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Last modified March 30 02:54 EDT 2023. Contains 361603 sequences. (Running on oeis4.)