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 A115437 Numbers n such that the concatenation of n with n+4 gives a square. 11

%I

%S 96,205,300,477,732,1920,3157,52896,120085,427020,8264460,88581312,

%T 112000885,112917765,143075580,152863360,193537077,233788192,

%U 266755221,313680096,370908477,386568925,440852992,442670220

%N Numbers n such that the concatenation of n with n+4 gives a square.

%C 1. a(n).(a(n)+4) = A115438^2 where dot denotes concatenation. 2. All numbers of the form f(n) = 4(n).2.6(n-1).70.2(n).0 where n>0 are in the sequence because if k(n) = 6(n).5.3(n).4.6(n).8 then k(n)^2 = f(n).(f(n)+4). For example f(4) = 444426667022220; k(4) = 666653333466668 and k(4)^2 = 666653333466668^2 = f(4).(f(4)+4) = 444426667022220.444426667022224. 3.All numbers of the form f(n) = 1(n).2.0(n+1).8(n).5 where n>-1 are in the sequence because if k(n) = 3(n).4.6(n).5.3(n+1) then k(n)^2 = f(n).(f(n)+4). For example f(5) = 111112000000888885; k(5) = 333334666665333333 and k(5)^2 = 333334666665333333^2 = f(5). (f(5)+4) = 111112000000888885.111112000000888889. - _Farideh Firoozbakht_, Nov 26 2006

%e 120085_120089 = 346533^2.

%Y Cf. A030465, A102567, A115426, A115428, A115429, A115430, A115431, A115432, A115433, A115434, A115435, A115436, A115438.

%K base,nonn

%O 1,1

%A _Giovanni Resta_, Jan 24 2006

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Last modified June 19 10:09 EDT 2021. Contains 345126 sequences. (Running on oeis4.)