A116287 - OEIS

%I #18 Apr 09 2025 07:23:41

%S 8,98,767,858,910,998,3285,6713,9998,45452,54546,99998,990100,999998,

%T 8181819,9999998,70588233,99999998,343130554,362637363,363636361,

%U 420053631,421052632,497975709,502024289,578947366,579946367,636363637,637362635,656869444,706766918,713286714,714285712,783689995

%N Numbers k such that k*(k+3) gives the concatenation of a number m with itself.

%C From _Robert Israel_, Apr 08 2025: (Start)

%C Numbers k such that k * (k + 3) = (10^d + 1) * m for some d and m where m has d digits.

%C Contains 10^d-2 for all d >= 1. (End)

%H Robert Israel, <a href="/A116287/b116287.txt">Table of n, a(n) for n = 1..10000</a>

%p q:= proc(d,m) local R,t,a,b,x,q;

%p    t:= 10^d+1;

%p    R:= NULL;

%p    for a in numtheory:-divisors(t) do

%p      b:= t/a;

%p      if igcd(a,b) > 1 then next fi;

%p      for x from chrem([0,-m],[a,b]) by t do

%p        q:= x*(x+m)/t;

%p        if q >= 10^d then break fi;

%p        if q >= 10^(d-1) then R:= R, x fi;

%p    od od;

%p    sort(convert({R},list));

%p end proc:

%p seq(op(q(d,3)),d=1..10); # _Robert Israel_, Apr 08 2025

%Y Cf. A116130, A116280, A116286, A116288, A116296.

%K nonn,base

%O 1,1

%A _Giovanni Resta_, Feb 06 2006

%E More terms from _Robert Israel_, Apr 08 2025