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A116341 k times k+8 gives the concatenation of two numbers m and m+7.

%I A116341 #13 Feb 22 2024 15:10:44
%S A116341 82,314,679,756,952,965,3205775326418807415637845823789043451,
%T A116341 3230931606745075612526180113373983267,
%U A116341 3750967203300732832735999247776048870,6249032796699267167264000752223951123,6769068393254924387473819886626016726,6794224673581192584362154176210956542
%N A116341 k times k+8 gives the concatenation of two numbers m and m+7.
%H A116341 Chai Wah Wu, <a href="/A116341/b116341.txt">Table of n, a(n) for n = 1..56</a>
%e A116341 965 * 973 = 938//945, where // denotes concatenation, so 965 is a term.
%o A116341 (Python)
%o A116341 from itertools import count, islice
%o A116341 from sympy import sqrt_mod
%o A116341 def A116341_gen(): # generator of terms
%o A116341     for j in count(0):
%o A116341         b = 10**j
%o A116341         a = b*10+1
%o A116341         for k in sorted(sqrt_mod(23,a,all_roots=True)):
%o A116341             if a*(b-7) <= k**2-23 < a*(a-8) and k>4:
%o A116341                 yield k-4
%o A116341 A116341_list = list(islice(A116341_gen(),20)) # _Chai Wah Wu_, Feb 21 2024
%Y A116341 Cf. A116210, A116333, A116340, A116342, A116354.
%K A116341 nonn,base
%O A116341 1,1
%A A116341 _Giovanni Resta_, Feb 06 2006
%E A116341 a(10)-a(12) from _Chai Wah Wu_, Feb 21 2024