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%I #16 Feb 21 2024 01:25:43
%S 7,97,451,546,689,854,997,4380,5617,9997,72728,99997,346531,653466,
%T 999997,9090906,9999997,94117644,99999997,334665331,336032385,
%U 378253326,390977440,439928489,483516484,516483513,560071508
%N Numbers k such that k*(k+4) gives the concatenation of a number m with itself.
%C Contains 10^m - 3 hence the sequence is infinite. - _David A. Corneth_, Feb 20 2024
%H Chai Wah Wu, <a href="/A116288/b116288.txt">Table of n, a(n) for n = 1..10000</a>
%o (Python)
%o from itertools import count, islice
%o from sympy import sqrt_mod
%o def A116288_gen(): # generator of terms
%o for j in count(0):
%o b = 10**j
%o a = b*10+1
%o for k in sorted(sqrt_mod(4,a,all_roots=True)):
%o if a*b <= k**2-4 < a*(a-1):
%o yield k-2
%o A116288_list = list(islice(A116288_gen(),40)) # _Chai Wah Wu_, Feb 20 2024
%Y Cf. A116125, A116275, A116287, A116289, A116297.
%K nonn,base
%O 1,1
%A _Giovanni Resta_, Feb 06 2006
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