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

%I #8 Feb 22 2024 01:50:56

%S 79,35475530,41357883,58642110,64524463,3317813164402425001808,

%T 3762581663871761671881,4019782237714250566387,4464550737183587236460,

%U 5535449262816412763533,5980217762285749433606,6237418336128238328112

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

%e 64524463 * 64524471 = 41634068//41634073, where // denotes concatenation, so 64524463 is a term.

%o (Python)

%o from itertools import count, islice

%o from sympy import sqrt_mod

%o def A116327_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(21,a,all_roots=True)):

%o if a*(b-5) <= k**2-21 < a*(a-6) and k>4:

%o yield k-4

%o A116327_list = list(islice(A116327_gen(),20)) # _Chai Wah Wu_, Feb 21 2024

%Y Cf. A116196, A116320, A116326, A116328, A116333.

%K nonn,base

%O 1,1

%A _Giovanni Resta_, Feb 06 2006