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A073630 Numbers k such that k*(prime(k) - 1) is a square. 0
1, 2, 8, 1849, 22912, 40328, 646912, 3607298, 6323422, 7520900, 8962893, 23879700, 38043325, 157944268, 1105942626, 3604734726, 5239828426, 8179002096, 8179002106, 37234260225 (list; graph; refs; listen; history; text; internal format)
OFFSET
1,2
COMMENTS
Next term is > 2.5*10^10. - Ryan Propper, Nov 10 2006
a(21) > pi(10^12). - Donovan Johnson, Feb 26 2010
LINKS
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
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
STATUS
approved

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Last modified June 15 13:08 EDT 2024. Contains 373407 sequences. (Running on oeis4.)