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A069521
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Smallest multiple of n with digit sum = 2, or 0 if no such number exists, e.g., a(3k)=0.
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22
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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
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OFFSET
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1,1
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COMMENTS
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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
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LINKS
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Robert Israel, Table of n, a(n) for n = 1..2016
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FORMULA
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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)
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EXAMPLE
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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.
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MAPLE
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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
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CROSSREFS
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Cf. A043292, A069531.
Sequence in context: A134085 A151339 A228273 * A245687 A228617 A119836
Adjacent sequences: A069518 A069519 A069520 * A069522 A069523 A069524
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KEYWORD
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base,nonn
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AUTHOR
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Amarnath Murthy, Apr 01 2002
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EXTENSIONS
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More terms from Ray Chandler, Jul 30 2003
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STATUS
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approved
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