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A116254 k times k+4 gives the concatenation of two numbers m and m-5.

%I A116254 #13 Feb 24 2024 22:04:00
%S A116254 89,9077,9899,733672,998999,88225293,99989999,8900869206,9296908810,
%T A116254 9604060395,9999899999,326666333265,673333666732,700730927006,
%U A116254 972603739725,999998999999,34519562953735,39737862788836,49917309624954,50082690375043,60262137211161,65480437046262
%N A116254 k times k+4 gives the concatenation of two numbers m and m-5.
%H A116254 Chai Wah Wu, <a href="/A116254/b116254.txt">Table of n, a(n) for n = 1..3000</a>
%o A116254 (Python)
%o A116254 from itertools import count, islice
%o A116254 from sympy import sqrt_mod
%o A116254 def A116254_gen(): # generator of terms
%o A116254     for j in count(0):
%o A116254         b = 10**j
%o A116254         a = b*10+1
%o A116254         for k in sorted(sqrt_mod(-1,a,all_roots=True)):
%o A116254             m = (k**2+1)//a
%o A116254             if a*(b+4) <= k**2+1 < a*(a+3):
%o A116254                 yield k-2
%o A116254 A116254_list = list(islice(A116254_gen(),40)) # _Chai Wah Wu_, Feb 19 2024
%Y A116254 Cf. A054214, A116248, A116253, A116255, A116260.
%K A116254 nonn,base
%O A116254 1,1
%A A116254 _Giovanni Resta_, Feb 06 2006
%E A116254 a(19)-a(22) from _Chai Wah Wu_, Feb 19 2024