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URL: https://oeis.org/A116286

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A116286
Numbers k such that k*(k+2) gives the concatenation of a number m with itself.
6
9, 99, 427, 572, 726, 845, 999, 7809, 9999, 36364, 63635, 99999, 326733, 673266, 999999, 4545453, 5454546, 9999999, 47058822, 52941177, 99999999, 331983806, 332667333, 384615385, 422892897, 475524476, 524475523, 577107102, 615384614, 667332666, 668016193, 719964245, 758241757, 804511279
OFFSET
1,1
COMMENTS
From Robert Israel, Apr 08 2025: (Start)
Numbers k such that k * (k + 2) = (10^d + 1) * m for some d and m where m has d digits.
Contains 10^d - 1 for all d >= 1. (End)
LINKS
MAPLE
q:= proc(d, m) local R, t, a, b, x, q;
t:= 10^d+1;
R:= NULL;
for a in numtheory:-divisors(t) do
b:= t/a;
if igcd(a, b) > 1 then next fi;
for x from chrem([0, -m], [a, b]) by t do
q:= x*(x+m)/t;
if q >= 10^d then break fi;
if q >= 10^(d-1) then R:= R, x fi;
od od;
sort(convert({R}, list));
end proc:
A:=[seq(op(q(d, 2)), d=1..10)]; # Robert Israel, Apr 08 2025
CROSSREFS
KEYWORD
nonn,base
AUTHOR
Giovanni Resta, Feb 06 2006
EXTENSIONS
More terms from Robert Israel, Apr 08 2025
STATUS
approved