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URL: https://oeis.org/A116291

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A116291
Numbers k such that k * (k + 7) is the concatenation of a number m with itself.
6
4, 94, 455, 539, 994, 7665, 9994, 72721, 99994, 356429, 643565, 999994, 9090910, 9999994, 35294118, 64705876, 99999994, 335664329, 664335665, 684210520, 818181819, 838056674, 846153847, 866028702, 980125139, 999999994
OFFSET
1,1
COMMENTS
From Robert Israel, Apr 09 2025: (Start)
Numbers k such that k * (k + 7) = (10^d + 1) * m for some d and m where m has d digits.
Contains 10^d - 6 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:
[seq(op(q(d, 7)), d=1..10)]; # Robert Israel, Apr 09 2025
CROSSREFS
KEYWORD
nonn,base
AUTHOR
Giovanni Resta, Feb 06 2006
STATUS
approved