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A115439 Numbers m such that the square of m is the concatenation of two numbers k and k+5.

%I A115439 #25 Jul 09 2023 11:21:14
%S A115439 4,7,45,56,38163,61838,83618,346980,653021,950051,8647555,9534265,
%T A115439 8167822283,9007920992,9209900792,9950000501,4737445289221,
%U A115439 4990568257187,5009431742814,5262554710780,8373808925585,8626931893551,34323166122692,34532758615690,49625657225895,49835249718893
%N A115439 Numbers m such that the square of m is the concatenation of two numbers k and k+5.
%C A115439 All numbers of the form f(n)=9(n).5.0(2n).5.0(n-1).1 where n>0 are in the sequence because if k(n)=9(n).0(n).25.0(n-1).9(n).6 then f(n)^2=k(n).(k(n)+5). For example f(2)=9950000501; k(2)=9900250996 and f(2)^2=9950000501^2=9900250996.9900251001 =k(2).(k(2)+5). - _Farideh Firoozbakht_, Nov 26 2006
%C A115439 m^2 = (k)|(k+5) = (k)|(k) + 5 = (10^q + 1)*k + 5 where | denotes concatenation and q is the number of digits of k gives a nonlinear equation that can be solved using the solver below. - _David A. Corneth_, Jan 02 2021
%H A115439 David A. Corneth, <a href="/A115439/b115439.txt">Table of n, a(n) for n = 1..3733</a>
%H A115439 Dario A. Alpern, <a href="https://www.alpertron.com.ar/QUAD.HTM">Generic two integer variable equation solver</a>
%e A115439 38163^2 = 14564_14569.
%Y A115439 Cf. A030467, A057934, A106497, A115428, A115427, A115438, A115440, A115441, A115442, A115443, A115444, A115445, A115446, A115447.
%K A115439 base,nonn
%O A115439 1,1
%A A115439 _Giovanni Resta_, Jan 24 2006
%E A115439 More terms from _David A. Corneth_, Jan 02 2021