A073630 - OEIS

%I #26 Oct 19 2024 18:08:48

%S 1,2,8,1849,22912,40328,646912,3607298,6323422,7520900,8962893,

%T 23879700,38043325,157944268,1105942626,3604734726,5239828426,

%U 8179002096,8179002106,37234260225,48548322900,57996680625,151600166550,628514460280

%N Numbers k such that k*(prime(k) - 1) is a square.

%C Next term is > 2.5*10^10. - _Ryan Propper_, Nov 10 2006

%C prime(a(21)) > 10^12. - _Donovan Johnson_, Feb 26 2010

%C a(25) > 10^12. - _Lucas A. Brown_, Oct 19 2024

%H Lucas A. Brown, <a href="https://github.com/lucasaugustus/oeis/blob/main/A073630.py">Python program</a>.

%e 7520900*(prime(7520900) - 1) = 997787845328400 = 31587780^2 is a perfect square, so 7520900 is in the sequence.

%t Do[k = n*Prime[n] - n; If[IntegerQ[Sqrt[k]], Print[n]], {n, 1, 670000000}] (* _Ryan Propper_, Aug 24 2005 *)

%o (PARI) isok(k) = issquare(k*(prime(k)-1)); \\ _Michel Marcus_, Feb 15 2021

%K nonn,hard,more

%O 1,2

%A _Benoit Cloitre_, Aug 29 2002

%E More terms from _Ryan Propper_, Aug 24 2005

%E More terms from _Ryan Propper_, Nov 10 2006

%E a(20) from _Donovan Johnson_, Feb 26 2010

%E a(21)-a(24) from _Lucas A. Brown_, Oct 19 2024