A073630 Numbers k such that k*(prime(k) - 1) is a square.

1, 2, 8, 1849, 22912, 40328, 646912, 3607298, 6323422, 7520900, 8962893, 23879700, 38043325, 157944268, 1105942626, 3604734726, 5239828426, 8179002096, 8179002106, 37234260225, 48548322900, 57996680625, 151600166550, 628514460280

Offset

1,2

Comments

Next term is > 2.5*10^10. - Ryan Propper, Nov 10 2006

prime(a(21)) > 10^12. - Donovan Johnson, Feb 26 2010

a(25) > 10^12. - Lucas A. Brown, Oct 19 2024

Links

Table of n, a(n) for n=1..24.

Lucas A. Brown, Python program.

Example

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

Mathematica

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

Prog

(PARI) isok(k) = issquare(k*(prime(k)-1)); \\ Michel Marcus, Feb 15 2021

Crossrefs

Sequence in context: A121015 A216619 A306241 * A027733 A054874 A174736

Adjacent sequences: A073627 A073628 A073629 * A073631 A073632 A073633

Keyword

nonn,hard,more

Author

Benoit Cloitre, Aug 29 2002

Extensions

More terms from Ryan Propper, Aug 24 2005

More terms from Ryan Propper, Nov 10 2006

a(20) from Donovan Johnson, Feb 26 2010

a(21)-a(24) from Lucas A. Brown, Oct 19 2024

Status

approved