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A049423 Primes of the form k^2 + 3. 16
3, 7, 19, 67, 103, 199, 487, 787, 1447, 2503, 2707, 3847, 4099, 4903, 5479, 5779, 8467, 8839, 11239, 12547, 14887, 16903, 17959, 19603, 21319, 23719, 24967, 25603, 29587, 31687, 47527, 52903, 58567, 59539, 61507, 65539, 75079, 81799, 88807 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

COMMENTS

Note that all terms after the first are congruent to 7 modulo 12.

LINKS

Vincenzo Librandi, Table of n, a(n) for n = 1..10000

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

FORMULA

Primes m such that m-3 is a square.

For n>0, a(n) = 36*A056902(n-1)^2 + 24*A056902(n-1) + 7. - Henry Bottomley, Jul 06 2000

EXAMPLE

19 is prime and is equal to 4^2 + 3, so 19 is a term.

MATHEMATICA

Intersection[Table[n^2+3, {n, 0, 10^2}], Prime[Range[9*10^3]]] ...or... For[i=3, i<=3, a={}; Do[If[PrimeQ[n^2+i], AppendTo[a, n^2+i]], {n, 0, 100}]; Print["n^2+", i, ", ", a]; i++ ] (* Vladimir Joseph Stephan Orlovsky, Apr 29 2008 *)

Select[Table[n^2+3, {n, 0, 198000}], PrimeQ] (* Vincenzo Librandi, Dec 08 2011 *)

PROG

(MAGMA) [n: n in PrimesUpTo(175000) | IsSquare(n-3)];  // Bruno Berselli, Apr 05 2011

(MAGMA) [a: n in [0..300] | IsPrime(a) where a is n^2+3]; // Vincenzo Librandi, Dec 08 2011

CROSSREFS

Cf. A002496, A056899. Note that apart from first term, all of (a(n)-7)/12 have to be terms of A001082 for a(n) to be prime.

Sequence in context: A210985 A160128 A051139 * A121825 A066237 A135741

Adjacent sequences:  A049420 A049421 A049422 * A049424 A049425 A049426

KEYWORD

easy,nonn

AUTHOR

Paul Jobling (paul.jobling(AT)whitecross.com)

STATUS

approved

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Last modified February 24 19:27 EST 2020. Contains 332209 sequences. (Running on oeis4.)