A091459 Numbers n such that n-1, n and n+1 can be expressed as a sum of 2 squares in at least 2 ways.

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

Offset

1,1

Comments

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).

Links

Table of n, a(n) for n=1..31.

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

Sequence in context: A217533 A045133 A049535 * A224574 A232861 A250672

Adjacent sequences: A091456 A091457 A091458 * A091460 A091461 A091462

Keyword

nonn

Author

Robin Garcia, Mar 02 2004

Extensions

Corrected and extended by Ray Chandler, Mar 26 2004

Status

approved