A106042 Numbers k such that k*prime(k)-2 is a perfect square.

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

Offset

1,2

Comments

Next term after 3905394 is greater than 2*10^9. - Ryan Propper, Jun 26 2005

No more terms below 3*10^11. - Amiram Eldar, Dec 27 2018

a(9) > 7.8*10^12, if it exists. - Giovanni Resta, Oct 15 2019

Links

Table of n, a(n) for n=1..8.

Example

1*2-2=0^2
2*3-2=2^2
51*233-2=109^2
402*2753-2=1052^2
1506*12611-2=4358^2
18258*203387-2=60938^2
3905394*66166537-2 = 16075024^2
4692517426*114590319401-2 = 23188727232^2

Mathematica

Select[Range[20000], IntegerQ[Sqrt[# * Prime[#] - 2]] &] (* Amiram Eldar, Dec 27 2018 *)

Prog

(PARI) isok(k) = issquare(k*prime(k)-2); \\ Michel Marcus, Dec 27 2018

Crossrefs

Cf. A106041.

Sequence in context: A078165 A180110 A037058 * A222850 A089304 A210907

Adjacent sequences: A106039 A106040 A106041 * A106043 A106044 A106045

Keyword

more,nonn

Author

Zak Seidov, May 06 2005

Extensions

a(7) from Ryan Propper, Jun 26 2005

a(8) from Amiram Eldar, Dec 27 2018

Status

approved