%I #16 Feb 21 2024 01:25:33
%S 8872,9009,83352840,99000099,329767122286,670232877711,738226276371,
%T 933006600339,999000000999,3779410975143113,3872816717528065,
%U 4250291784692548,4278630943941865,4372036686326817,4749511753491300,5250488246508697,5627963313673180,5721369056058132
%N Numbers k such that k*(k+4) gives the concatenation of two numbers m and m-2.
%H Chai Wah Wu, <a href="/A116275/b116275.txt">Table of n, a(n) for n = 1..1187</a>
%e 99000099 * 99000103 = 98010199//98010197, where // denotes concatenation.
%o (Python)
%o from itertools import count, islice
%o from sympy import sqrt_mod
%o def A116275_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(2,a,all_roots=True)):
%o if a*(b+3) <= k**2-2 < a*(a+2):
%o yield k-2
%o A116275_list = list(islice(A116275_gen(),30)) # _Chai Wah Wu_, Feb 19 2024
%Y Cf. A115426, A116267, A116274, A116276, A116288.
%K nonn,base
%O 1,1
%A _Giovanni Resta_, Feb 06 2006
%E a(16)-a(18) from _Chai Wah Wu_, Feb 19 2024
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