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Numbers k such that k^2+1 = 2*p^2, p prime.
4

%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