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A028874 Primes of form n^2 - 3. 3
13, 61, 97, 193, 397, 673, 1021, 1153, 1597, 1933, 2113, 3361, 4093, 4621, 6397, 7393, 7741, 8461, 9601, 12097, 12541, 13921, 15373, 16381, 18493, 19597, 20161, 21313, 26893, 29581, 36097, 37633, 40801, 42433, 43261, 47521, 48397 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

COMMENTS

Also primes equal to the product of two consecutive odd numbers minus 2. - Giovanni Teofilatto, Feb 11 2010

All terms are of the form 6m+1. - Zak Seidov, May 01 2014

LINKS

Nathaniel Johnston, Table of n, a(n) for n = 1..10000

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

R. J. Mathar, Solutions to the exponential Diophantine 1 + p_1^x + p_2^y + p_3^z = w^2 for distinct primes p_1, p_2. p_3, 2014

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

EXAMPLE

a(2) = 61 = 8^2 - 3 = A028873(2)^2 - 3.

MATHEMATICA

lst={}; Do[s=n^2; If[PrimeQ[p=s-3], AppendTo[lst, p]], {n, 6!}]; lst (* Vladimir Joseph Stephan Orlovsky, Sep 26 2008 *)

Select[Range[2, 250]^2-3, PrimeQ] (* Harvey P. Dale, Aug 07 2013 *)

Select[Table[n^2 - 3, {n, 2, 300}], PrimeQ] (* Vincenzo Librandi, Nov 08 2014 *)

PROG

(MAGMA) [a: n in [2..300] | IsPrime(a) where a is n^2-3 ]; // Vincenzo Librandi, Nov 08 2014

(PARI) select(isprime, vector(100, n, n^2-3)) \\ Charles R Greathouse IV, Nov 19 2014

CROSSREFS

Cf. A028871, A002476 (Primes of form 6m+1).

Sequence in context: A217606 A002647 A118711 * A087106 A142402 A140615

Adjacent sequences:  A028871 A028872 A028873 * A028875 A028876 A028877

KEYWORD

nonn

AUTHOR

Patrick De Geest

STATUS

approved

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Last modified December 12 20:04 EST 2017. Contains 295954 sequences.