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URL: https://oeis.org/A116289

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A116289
Numbers k such that k*(k+5) gives the concatenation of a number m with itself.
6
6, 96, 385, 429, 567, 611, 814, 996, 4521, 5475, 9996, 90910, 99996, 316832, 683164, 999996, 3636364, 6363632, 9999996, 82352942, 99999996, 331668332, 368421053, 395604391, 442767754, 461538462, 488721800, 511278196, 538461534, 557232242, 604395605, 631578943, 668331664, 700089385, 727272728
OFFSET
1,1
COMMENTS
From Robert Israel, Apr 09 2025: (Start)
Numbers k such that k * (k + 5) = (10^d + 1) * m for some d and m where m has d digits.
Contains 10^d-4 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, 5)), d=1..10); # Robert Israel, Apr 09 2025
CROSSREFS
KEYWORD
nonn,base
AUTHOR
Giovanni Resta, Feb 06 2006
EXTENSIONS
More terms from Robert Israel, Apr 09 2025
STATUS
approved