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A117475 The values of c in a^2 + b^2 = c^2 where b - a = 23 and gcd(a,b,c) = 1. 1

%I

%S 37,65,205,373,1193,2173,6953,12665,40525,73817,236197,430237,1376657,

%T 2507605,8023745,14615393,46765813,85184753,272571133,496493125,

%U 1588660985,2893773997,9259394777,16866150857,53967707677,98303131145

%N The values of c in a^2 + b^2 = c^2 where b - a = 23 and gcd(a,b,c) = 1.

%C b - a = 23 is the fourth term in A058529. The values of a are in A117476.

%H <a href="/index/Rec#order_04">Index entries for linear recurrences with constant coefficients</a>, signature (0,6,0,-1).

%F c(1)=37, c(2)=65, c(3)=205, c(4)=373, c(n) = 6*c(n-2) - c(n-4).

%F G.f.: -x*(17*x^3+17*x^2-65*x-37) / ((x^2-2*x-1)*(x^2+2*x-1)). [_Colin Barker_, Dec 17 2012]

%e c(5) = 6*205 - 37 = 1193 and 832^2 + 855^2 = 1193^2 and 855-832=23 and gcd(832,855,1193)=1.

%Y Cf. A058529, A117476.

%K nonn,easy,changed

%O 1,1

%A Andras Erszegi (erszegi.andras(AT)chello.hu), Mar 19 2006

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Last modified May 6 19:52 EDT 2021. Contains 343586 sequences. (Running on oeis4.)