A050796 Numbers n such that n^2 + 1 is expressible as the sum of two nonzero squares in at least one way (the trivial solution n^2 + 1 = n^2 + 1^2 is not counted).

1, 7, 8, 12, 13, 17, 18, 21, 22, 23, 27, 28, 30, 31, 32, 33, 34, 37, 38, 41, 42, 43, 44, 46, 47, 48, 50, 52, 53, 55, 57, 58, 60, 62, 63, 64, 67, 68, 70, 72, 73, 75, 76, 77, 78, 80, 81, 82, 83, 86, 87, 88, 89, 91, 92, 93, 96, 97, 98, 99, 100, 102, 103, 104, 105, 106, 107

Offset: 1

Author

Patrick De Geest, Sep 15 1999

Keywords

• nonn

Comments

Analogous solutions exist for the sum of two identical squares z^2 + 1 = 2*r^2 (e.g., 41^2 + 1 = 2*29^2). Values of 'z' are the terms in sequence A002315, values of 'r' are the terms in sequence A001653.

Apart from the first term, numbers n such that (n^2)! == 0 mod (n^2 + 1)^2. - Michel Lagneau, Feb 14 2012

Numbers n such that neither n^2 + 1 nor (n^2 + 1)/2 is prime. - Charles R Greathouse IV, Feb 14 2012

Examples

			E.g., 57^2 + 1 = 15^2 + 55^2 = 21^2 + 53^2 = 35^2 + 45^2.
		

Links

• Charles R Greathouse IV, Table of n, a(n) for n = 1..10000
• Index entries for sequences related to sums of squares

Crossrefs

Cf. A000129, A001653, A002315, A050795, A050798.

Programs

Mathematica

t={1}; Do[i=c=2; While[iJayanta Basu, Jun 01 2013 *)

PARI

is(n)=!isprime((n^2+1)/if(n%2,2,1)) \\ Charles R Greathouse IV, Feb 14 2012