|
%I #13 Feb 11 2024 09:16:44
%S 0,11,263,59,23,101,109,1278886952463697,151,193,79,269,277,311,0,179,
%T 83,83003,479,487,181,563,571,613,1201,157,141509,739,773,479,
%U 6858037981,907,1291,983,227,6133,1109,1151,54331,1201,431,307,1327
%N For p = the n-th prime, a(n) = the least prime q greater than p+2 such that (p^2+q^2)/2 - 1 is a square, or a(n) = 0 if there is no such prime.
%H Don Reble, <a href="/A130177/b130177.txt">Table of n, a(n) for n=1..787</a>
%H Dean Hickerson, <a href="/A130177/a130177.txt">Proof that a(15) = 0</a>
%H Number Theory Web, <a href="http://www.numbertheory.org/php/patz.html">Solving x^2-Dy^2=N</a>
%H J. P. Robertson, <a href="https://web.archive.org/web/20180831180333/http://www.jpr2718.org/pell.pdf">Solving the Generalized Pell Equation</a>
%e a(3) = 263 because (5^2+263^2)/2-1 = 186^2.
%e a(4) = 59 because (7^2+59^2)/2-1 = 42^2.
%e a(5) = 23 because (11^2+23^2)/2-1 = 18^2.
%K nonn
%O 1,2
%A _Nick Hobson_, May 14 2007
%E Edited by _T. D. Noe_ and _Don Reble_, May 14 2007
|
