A050798 - OEIS

%I #19 Jul 03 2017 02:05:23

%S 1,7,8,12,13,17,21,22,23,27,28,30,31,33,34,37,41,42,44,46,48,50,52,53,

%T 55,58,60,62,63,64,67,75,76,77,78,80,81,86,87,88,89,91,92,96,97,100,

%U 102,103,104,105,106,108,109,111,113,114,115,119,125,127,129,135,136

%N Numbers n such that m = n^2 + 1 is expressible as the sum of two nonzero squares in exactly two ways.

%C Of course m = n^2 + 1 is the sum of two squares, by definition. Here there should be just one other way to write m as a different sum of two squares.

%C Let p and q be primes of the form 1+4k. Then n^2+1 must be pq or 2pq. - _T. D. Noe_, May 27 2008

%H T. D. Noe, <a href="/A050798/b050798.txt">Table of n, a(n) for n=1..1000</a>

%H Eric Weisstein, <a href="http://mathworld.wolfram.com/SumofSquaresFunction.html">MathWorld: Sum of Squares Function</a>

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

%e E.g., 111^2 + 1 = 21^2 + 109^2 only.

%t ok[1] = True; ok[n_] := Length[ {ToRules[ Reduce[ 1 < x <= y && n^2 + 1 == x^2 + y^2, {x, y}, Integers] ] } ] == 1; Select[ Range[136], ok] (* _Jean-François Alcover_, Feb 16 2012 *)

%Y Cf. A000161, A050797, A050796.

%K nonn,nice

%O 1,2

%A _Patrick De Geest_, Sep 15 1999

%E Better definition from _T. D. Noe_, May 27 2008