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A116275 Numbers k such that k*(k+4) gives the concatenation of two numbers m and m-2.

%I A116275 #16 Feb 21 2024 01:25:33
%S A116275 8872,9009,83352840,99000099,329767122286,670232877711,738226276371,
%T A116275 933006600339,999000000999,3779410975143113,3872816717528065,
%U A116275 4250291784692548,4278630943941865,4372036686326817,4749511753491300,5250488246508697,5627963313673180,5721369056058132
%N A116275 Numbers k such that k*(k+4) gives the concatenation of two numbers m and m-2.
%H A116275 Chai Wah Wu, <a href="/A116275/b116275.txt">Table of n, a(n) for n = 1..1187</a>
%e A116275 99000099 * 99000103 = 98010199//98010197, where // denotes concatenation.
%o A116275 (Python)
%o A116275 from itertools import count, islice
%o A116275 from sympy import sqrt_mod
%o A116275 def A116275_gen(): # generator of terms
%o A116275     for j in count(0):
%o A116275         b = 10**j
%o A116275         a = b*10+1
%o A116275         for k in sorted(sqrt_mod(2,a,all_roots=True)):
%o A116275             if a*(b+3) <= k**2-2 < a*(a+2):
%o A116275                 yield k-2
%o A116275 A116275_list = list(islice(A116275_gen(),30)) # _Chai Wah Wu_, Feb 19 2024
%Y A116275 Cf. A115426, A116267, A116274, A116276, A116288.
%K A116275 nonn,base
%O A116275 1,1
%A A116275 _Giovanni Resta_, Feb 06 2006
%E A116275 a(16)-a(18) from _Chai Wah Wu_, Feb 19 2024