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A116327 k times k+8 gives the concatenation of two numbers m and m+5.

%I A116327 #8 Feb 22 2024 01:50:56
%S A116327 79,35475530,41357883,58642110,64524463,3317813164402425001808,
%T A116327 3762581663871761671881,4019782237714250566387,4464550737183587236460,
%U A116327 5535449262816412763533,5980217762285749433606,6237418336128238328112
%N A116327 k times k+8 gives the concatenation of two numbers m and m+5.
%e A116327 64524463 * 64524471 = 41634068//41634073, where // denotes concatenation, so 64524463 is a term.
%o A116327 (Python)
%o A116327 from itertools import count, islice
%o A116327 from sympy import sqrt_mod
%o A116327 def A116327_gen(): # generator of terms
%o A116327     for j in count(0):
%o A116327         b = 10**j
%o A116327         a = b*10+1
%o A116327         for k in sorted(sqrt_mod(21,a,all_roots=True)):
%o A116327             if a*(b-5) <= k**2-21 < a*(a-6) and k>4:
%o A116327                 yield k-4
%o A116327 A116327_list = list(islice(A116327_gen(),20)) # _Chai Wah Wu_, Feb 21 2024
%Y A116327 Cf. A116196, A116320, A116326, A116328, A116333.
%K A116327 nonn,base
%O A116327 1,1
%A A116327 _Giovanni Resta_, Feb 06 2006