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A116202 Numbers k such that k concatenated with k+6 gives the product of two numbers which differ by 8.

%I A116202 #17 Feb 22 2024 14:38:32
%S A116202 7,54,234,267,894,58227,7962242238271227055830015496107,
%T A116202 60153956829051761181170060654114714579377214308482459,
%U A116202 2019668016997743800626449453386765007975459365956534868322001037107,3031524678136833532602149525055953135725227119574025423809994922862
%N A116202 Numbers k such that k concatenated with k+6 gives the product of two numbers which differ by 8.
%H A116202 Chai Wah Wu, <a href="/A116202/b116202.txt">Table of n, a(n) for n = 1..16</a>
%e A116202 58227//58233 = 76303 * 76311, where // denotes concatenation.
%o A116202 (Python)
%o A116202 from itertools import count, islice
%o A116202 from sympy import sqrt_mod
%o A116202 def A116202_gen(): # generator of terms
%o A116202     for j in count(0):
%o A116202         b = 10**j
%o A116202         a = b*10+1
%o A116202         for k in sorted(sqrt_mod(22,a,all_roots=True)):
%o A116202             if a*(b-6) <= k**2-22 < a*(a-7) and k>4:
%o A116202                 yield (k**2-22)//a
%o A116202 A116202_list = list(islice(A116202_gen(),7)) # _Chai Wah Wu_, Feb 21 2024
%Y A116202 Cf. A116196, A116147, A116203, A116210, A116333.
%K A116202 nonn,base
%O A116202 1,1
%A A116202 _Giovanni Resta_, Feb 06 2006
%E A116202 a(8)-a(10) from _Chai Wah Wu_, Feb 21 2024