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%I #19 Sep 14 2015 16:07:42
%S 7,41,8119,47321,63018038201,2470433131948081,96845919575610633161,
%T 19175002942688032928599,5834531641231893991002972081099601,
%U 6733044458057842709277507685523012161,228725309250740208744750893347264645481
%N Numbers k such that k^2+1 = 2*p^2, p prime.
%C Subset of A002315 (Numbers k such that k^2 + 1 = 2*q^2).
%H Charles R Greathouse IV, <a href="/A183064/b183064.txt">Table of n, a(n) for n = 1..22</a>
%e a(2) = 41 because 41^2+1 = 2*29^2.
%p with(numtheory):for n from 1 to 1000000 do : p:=ithprime(n):x:=2*p^2: y:=sqrt(x-1):if
%p y=floor(y) then print(y):else fi:od:
%o (PARI) list(lim)=my(v=List(),w=3+quadgen(32),k,n); while((k=imag((1+w)*w^n++))<=lim, if(ispseudoprime(sqrtint((k^2+1)/2)), listput(v,k))); Vec(v) \\ _Charles R Greathouse IV_, Sep 14 2015
%Y Cf. A002315, A005574, A002731, A174492.
%K nonn
%O 1,1
%A _Michel Lagneau_, Feb 01 2011
%E More terms from _Charles R Greathouse IV_, Feb 01 2011
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