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A110732
Let n = abc... where a,b,c ... are the digits. Then a(n) = least multiple of n of the form aaa...bbb...ccc..., with each digit having the same frequency f > 1; or 0 if no such number exists.
2
11, 22, 33, 44, 55, 66, 77, 88, 99, 1100, 1111, 0, 111111333333, 111111444444, 1155, 0, 11111111111111117777777777777777, 1188, 111111111111111111999999999999999999, 2200, 222222111111, 2222, 22222222222222222222223333333333333333333333, 0, 0
OFFSET
1,1
COMMENTS
For odd n not a multiple of 5, a(n) is not 0, as every such odd number divides a (infinitely many) unary number of the type 11111...= (10^k-1)/9, by Fermat's little theorem. E.g., 13 divides 111111, hence a(13) = 111111333333. Zeros occur only for some powers/multiples of 2 and 5 as 25 does not divide 222555... etc. and 16 cannot divide any number of the type 111...666...
REFERENCES
Amarnath Murthy, On the divisors of unary sequence, Smarandache Notions Journal, Vol-11, 2000.
LINKS
MAPLE
f:= proc(n) local x, L, i, m, eq, S;
L:= convert(n, base, 10);
eq:= add(L[i]*10^(i*m)*(1-10^(-m))/9, i=1..nops(L));
S:= map(t -> rhs(op(t)), {msolve(eq, n)}) minus {0, 1};
if S = {} then 0
elif S = {m} then eval(eq, m=2)
else eval(eq, m = min(S))
fi
end proc:
map(f, [$1..30]); # Robert Israel, Aug 18 2024
CROSSREFS
Cf. A110733.
Sequence in context: A020338 A052191 A321536 * A044836 A338754 A033008
KEYWORD
base,easy,nonn
AUTHOR
Amarnath Murthy, Aug 09 2005
EXTENSIONS
More terms from Franklin T. Adams-Watters, Jun 06 2006
STATUS
approved