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A116333 k times k+8 gives the concatenation of two numbers m and m+6.

%I A116333 #15 Feb 22 2024 14:38:08
%S A116333 23,70,480,513,942,76303,8923139715521228493004072379869,
%T A116333 77558981961505761619171327422086381910161500424346805,
%U A116333 4494071669430455134012149964165405936125116123191254722256003057119,5505928330569544865987850035834594063874883876808745277743996942874
%N A116333 k times k+8 gives the concatenation of two numbers m and m+6.
%H A116333 Chai Wah Wu, <a href="/A116333/b116333.txt">Table of n, a(n) for n = 1..16</a>
%e A116333 76303 * 76311 = 58227//58233, where // denotes concatenation, so 76303 is a term.
%o A116333 (Python)
%o A116333 from itertools import count, islice
%o A116333 from sympy import sqrt_mod
%o A116333 def A116333_gen(): # generator of terms
%o A116333     for j in count(0):
%o A116333         b = 10**j
%o A116333         a = b*10+1
%o A116333         for k in sorted(sqrt_mod(22,a,all_roots=True)):
%o A116333             if a*(b-6) <= k**2-22 < a*(a-7) and k>4:
%o A116333                 yield k-4
%o A116333 A116333_list = list(islice(A116333_gen(),10)) # _Chai Wah Wu_, Feb 21 2024
%Y A116333 Cf. A116202, A116327, A116332, A116334, A116341.
%K A116333 nonn,base
%O A116333 1,1
%A A116333 _Giovanni Resta_, Feb 06 2006
%E A116333 a(8)-a(10) from _Chai Wah Wu_, Feb 21 2024