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URL: https://oeis.org/A116293

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A116293
Numbers k such that k * (k+9) is the concatenation of a number m with itself.
5
2, 92, 420, 572, 693, 728, 992, 9855, 9992, 36355, 63637, 99992, 970298, 999992, 4545455, 5454537, 9999992, 88235295, 99999992, 351069983, 403018035, 493927126, 506072866, 596981957, 648930009, 736842097, 739839100, 766233767, 769230761, 827751188, 857142858, 860139852, 879699240, 909090910
OFFSET
1,1
COMMENTS
From Robert Israel, Apr 09 2025: (Start)
Numbers k such that k * (k + 9) = (10^d + 1) * m for some d and m where m has d digits.
Contains 10^d-8 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, 9)), d=1..10)
CROSSREFS
KEYWORD
nonn,base
AUTHOR
Giovanni Resta, Feb 06 2006
EXTENSIONS
Name edited and more terms from Robert Israel, Apr 09 2025
STATUS
approved