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 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 (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 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) Eric Weisstein's World of Mathematics, Near-Square 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^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. 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 STATUS approved

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Last modified May 17 09:03 EDT 2021. Contains 343969 sequences. (Running on oeis4.)