

A091459


Numbers n such that n1, n and n+1 can be expressed as a sum of 2 squares in at least 2 ways.


2



22049, 26281, 26441, 29521, 34281, 47889, 51209, 56745, 66249, 68561, 72593, 74665, 84241, 92241, 96841, 98569, 100369, 103121, 103689, 105481, 105705, 109225, 109513, 117449, 119249, 124073, 125801, 126801, 135441, 139465, 141201
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OFFSET

1,1


COMMENTS

n must be of the form 4k+1 since if n is even, n1 or n+1 would be 4k+3, thus n+2 and n2 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 n1 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 n1=2^u*3^s*(4k+1)*(4k+3)^t (s>=2,t>=0;s and t even,u>=3) (only one of n1,n,n+1 must be a multiple of an even power of 3).


LINKS



EXAMPLE

We denote a^2+b^2=c^2+d^2 as (a,b,c,d)
34280=(182,34,166,82)
34281=(165,84,141,120)
34282=(181,39,171,71)


CROSSREFS



KEYWORD

nonn


AUTHOR



EXTENSIONS



STATUS

approved



