A106042 - OEIS

%I #11 Oct 15 2019 03:16:45

%S 1,2,51,402,1506,18258,3905394,4692517426

%N Numbers k such that k*prime(k)-2 is a perfect square.

%C Next term after 3905394 is greater than 2*10^9. - _Ryan Propper_, Jun 26 2005

%C No more terms below 3*10^11. - _Amiram Eldar_, Dec 27 2018

%C a(9) > 7.8*10^12, if it exists. - _Giovanni Resta_, Oct 15 2019

%e 1*2-2=0^2

%e 2*3-2=2^2

%e 51*233-2=109^2

%e 402*2753-2=1052^2

%e 1506*12611-2=4358^2

%e 18258*203387-2=60938^2

%e 3905394*66166537-2 = 16075024^2

%e 4692517426*114590319401-2 = 23188727232^2

%t Select[Range[20000], IntegerQ[Sqrt[# * Prime[#] - 2]] &] (* _Amiram Eldar_, Dec 27 2018 *)

%o (PARI) isok(k) = issquare(k*prime(k)-2); \\ _Michel Marcus_, Dec 27 2018

%Y Cf. A106041.

%K more,nonn

%O 1,2

%A _Zak Seidov_, May 06 2005

%E a(7) from _Ryan Propper_, Jun 26 2005

%E a(8) from _Amiram Eldar_, Dec 27 2018