A050796 - OEIS

%I #25 Oct 03 2017 02:02:36

%S 1,7,8,12,13,17,18,21,22,23,27,28,30,31,32,33,34,37,38,41,42,43,44,46,

%T 47,48,50,52,53,55,57,58,60,62,63,64,67,68,70,72,73,75,76,77,78,80,81,

%U 82,83,86,87,88,89,91,92,93,96,97,98,99,100,102,103,104,105,106,107

%N 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).

%C 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.

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

%C Numbers n such that neither n^2 + 1 nor (n^2 + 1)/2 is prime. - _Charles R Greathouse IV_, Feb 14 2012

%H Charles R Greathouse IV, <a href="/A050796/b050796.txt">Table of n, a(n) for n = 1..10000</a>

%H <a href="/index/Su#ssq">Index entries for sequences related to sums of squares</a>

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

%t 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 *)

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

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

%K nonn

%O 1,2

%A _Patrick De Geest_, Sep 15 1999