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

1,2

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

Links

Charles R Greathouse IV, Table of n, a(n) for n = 1..10000

Index entries for sequences related to sums of squares

Example

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

Mathematica

t={1}; Do[i=c=2; While[i<n&&c!=0, If[IntegerQ[Sqrt[n^2+1-i^2]], c=0; AppendTo[t, n]]; i++], {n, 3, 107}]; t (* Jayanta Basu, Jun 01 2013 *)

Prog

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

Crossrefs

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

Sequence in context: A348784 A294483 A105740 * A106630 A050798 A260628

Adjacent sequences: A050793 A050794 A050795 * A050797 A050798 A050799

Keyword

nonn

Author

Patrick De Geest, Sep 15 1999

Status

approved