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A116196 Numbers k such that k concatenated with k+5 gives the product of two numbers which differ by 8.

%I A116196 #13 Feb 22 2024 02:17:42
%S A116196 68,12585135,17104748,34388975,41634068,1100788419388203283323,
%T A116196 1415702077730399453204,1615864923864298764860,1993221328488651223275,
%U A116196 3064119854121476750348,3576300448435797632079,3890538749986876109435
%N A116196 Numbers k such that k concatenated with k+5 gives the product of two numbers which differ by 8.
%e A116196 41634068//41634073 = 64524463 * 64524471, where // denotes concatenation.
%o A116196 (Python)
%o A116196 from itertools import count, islice
%o A116196 from sympy import sqrt_mod
%o A116196 def A116196_gen(): # generator of terms
%o A116196     for j in count(0):
%o A116196         b = 10**j
%o A116196         a = b*10+1
%o A116196         for k in sorted(sqrt_mod(21,a,all_roots=True)):
%o A116196             if a*(b-5) <= k**2-21 < a*(a-6) and k>4:
%o A116196                 yield (k**2-21)//a
%o A116196 A116196_list = list(islice(A116196_gen(),10)) # _Chai Wah Wu_, Feb 21 2024
%Y A116196 Cf. A116189, A116195, A116197, A116202, A116327.
%K A116196 nonn,base
%O A116196 1,1
%A A116196 _Giovanni Resta_, Feb 06 2006