A183064 Numbers k such that k^2+1 = 2*p^2, p prime.

7, 41, 8119, 47321, 63018038201, 2470433131948081, 96845919575610633161, 19175002942688032928599, 5834531641231893991002972081099601, 6733044458057842709277507685523012161, 228725309250740208744750893347264645481

Offset: 1

Author

Michel Lagneau, Feb 01 2011

Keywords

• nonn

Comments

Subset of A002315 (Numbers k such that k^2 + 1 = 2*q^2).

Examples

			a(2) = 41 because 41^2+1 = 2*29^2.
		

Links

• Charles R Greathouse IV, Table of n, a(n) for n = 1..22

Crossrefs

Cf. A002315, A005574, A002731, A174492.

Programs

Maple

with(numtheory):for n from 1 to 1000000 do : p:=ithprime(n):x:=2*p^2: y:=sqrt(x-1):if
  y=floor(y) then print(y):else fi:od:

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

Extensions

More terms from Charles R Greathouse IV, Feb 01 2011