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A028877 Primes of form k^2 - 5. 4
11, 31, 59, 139, 191, 251, 479, 571, 1019, 1151, 1291, 1439, 1759, 1931, 2111, 2699, 3359, 4091, 5179, 5471, 6079, 6719, 8831, 10399, 12539, 13451, 14879, 17419, 20731, 23099, 26891, 27551, 28219, 30271, 30971, 33119, 33851, 34591 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

COMMENTS

These numbers are prime in Z but not in Z[sqrt(5)] nor in Z[phi] (where phi is the golden ratio), since (k - sqrt(5))(k + sqrt(5)) = ((k + 1) - 2*phi)((k - 1) + 2*phi) = k^2 - 5. - Alonso del Arte, Aug 27 2013

LINKS

Vincenzo Librandi, Table of n, a(n) for n = 1..8000

P. De Geest, Palindromic Quasipronics of the form n(n+x)

Eric Weisstein's World of Mathematics, Near-Square Prime

EXAMPLE

31 is in the sequence as it is equal to 6^2 - 5.

59 is in the sequence since it is equal to 8^2 - 5.

95 is not in the sequence though it does equal 10^2 - 5.

MATHEMATICA

Select[Table[n^2 - 5, {n, 200}], PrimeQ] (* Harvey P. Dale, Jan 17 2011 *)

PROG

(Magma) [a: n in [1..300] | IsPrime(a) where a is n^2-5]; // Vincenzo Librandi, Dec 01 2011

CROSSREFS

Cf. A028875 (superset), A028876.

Sequence in context: A144364 A226922 A031372 * A087394 A196117 A040162

Adjacent sequences: A028874 A028875 A028876 * A028878 A028879 A028880

KEYWORD

nonn,easy

AUTHOR

Patrick De Geest

STATUS

approved

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Last modified November 27 07:59 EST 2022. Contains 358362 sequences. (Running on oeis4.)