

A028874


Primes of form n^2  3.


4



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
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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
Primes of A028872.  Klaus Purath, Dec 07 2020


LINKS

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


EXAMPLE

61 is prime and equal to 8^2  3, so it is in the sequence.
67 is prime but it's 8^2 + 3 = 9^2  14, so it is not in the sequence.
9^2  3 = 78 but it's composite, so it's not in the sequence either.


MATHEMATICA

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^23 ]; // Vincenzo Librandi, Nov 08 2014
(PARI) select(isprime, vector(100, n, n^23)) \\ Charles R Greathouse IV, Nov 19 2014


CROSSREFS

Cf. A002476 (Primes of form 6m + 1), A028871, A028872.
Sequence in context: A118711 A316309 A317264 * A087106 A142402 A140615
Adjacent sequences: A028871 A028872 A028873 * A028875 A028876 A028877


KEYWORD

nonn


AUTHOR

Patrick De Geest


STATUS

approved



