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A116260 n times n+4 gives the concatenation of two numbers m and m-4.

%I A116260 #13 Feb 20 2024 00:49:11
%S A116260 9,99,999,9999,99999,999999,9999999,99999999,999999999,9999999999,
%T A116260 36363636362,45454545453,54545454544,63636363635,72727272726,
%U A116260 81818181817,90909090908,99999999999,999999999999,9999999999999
%N A116260 n times n+4 gives the concatenation of two numbers m and m-4.
%H A116260 Chai Wah Wu, <a href="/A116260/b116260.txt">Table of n, a(n) for n = 1..121</a>
%F A116260 10^d-1 for d>0 are terms. - _Chai Wah Wu_, Feb 19 2024
%e A116260 99999999 * 100000003 = 100000001//99999997, where // denotes concatenation.
%o A116260 (Python)
%o A116260 from itertools import count, islice
%o A116260 from sympy import sqrt_mod
%o A116260 def A116260_gen(): # generator of terms
%o A116260     for j in count(0):
%o A116260         b = 10**j
%o A116260         a = b*10+1
%o A116260         for k in sorted(sqrt_mod(0,a,all_roots=True))+[a]:
%o A116260             if a*(b+4) <= k**2 < a*(a+3):
%o A116260                 yield k-2
%o A116260 A116260_list = list(islice(A116260_gen(),20)) # _Chai Wah Wu_, Feb 19 2024
%Y A116260 Cf. A116129, A116254, A116259, A116261, A116267.
%K A116260 nonn,base
%O A116260 1,1
%A A116260 _Giovanni Resta_, Feb 06 2006