%I #6 Mar 31 2012 20:08:02

%S 22049,26281,26441,29521,34281,47889,51209,56745,66249,68561,72593,

%T 74665,84241,92241,96841,98569,100369,103121,103689,105481,105705,

%U 109225,109513,117449,119249,124073,125801,126801,135441,139465,141201

%N Numbers n such that n-1, n and n+1 can be expressed as a sum of 2 squares in at least 2 ways.

%C n must be of the form 4k+1 since if n is even, n-1 or n+1 would be 4k+3, thus n+2 and n-2 are 4k+3 and therefore: 3 is the maximum number of consecutive integers which can be expressed as a sum of 2 squares in at least 2 ways. n or n-1 or n+1 must be of the following forms: n=3^s*(4k+1)*(4k+3)^t or n+1=2*3^s*(4k+1)*(4k+3)^t or n-1=2^u*3^s*(4k+1)*(4k+3)^t (s>=2,t>=0;s and t even,u>=3) (only one of n-1,n,n+1 must be a multiple of an even power of 3).

%e We denote a^2+b^2=c^2+d^2 as (a,b,c,d)

%e 34280=(182,34,166,82)

%e 34281=(165,84,141,120)

%e 34282=(181,39,171,71)

%K nonn

%O 1,1

%A _Robin Garcia_, Mar 02 2004

%E Corrected and extended by _Ray Chandler_, Mar 26 2004