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A110284
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Squares of the form 4p - 3, where p is a prime.
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8
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9, 25, 49, 121, 169, 289, 625, 841, 961, 1225, 1681, 1849, 2401, 3025, 4489, 5929, 6889, 10201, 11881, 13225, 14161, 15625, 17689, 19321, 20449, 22801, 24025, 24649, 25921, 32041, 32761, 39601, 41209, 44521, 48841, 49729, 55225, 57121, 69169
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OFFSET
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1,1
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COMMENTS
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Squares are less dense then primes and easy to generate so it's faster to check squares if they are of the required form than to check if primes are of the required form. - David A. Corneth, Oct 15 2018
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LINKS
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FORMULA
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MATHEMATICA
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Select[ 4Prime[ Range[2000]] - 3, IntegerQ[ Sqrt[ # ]] &] (* Robert G. Wilson v, Sep 20 2005 *)
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PROG
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(PARI) isok(n) = issquare(n) && (p=(n+3)/4) && (frac(p)==0) && isprime(p); \\ Michel Marcus, Oct 15 2018
(PARI) upto(n) = my(res = List()); forstep(i = 3, sqrtint(n), 2, if(isprime((i^2+3)/4), listput(res, i^2))); res \\ David A. Corneth, Oct 15 2018
(Magma) [4*p - 3: p in PrimesUpTo(10^5)|IsSquare (4*p - 3)]; // Vincenzo Librandi, Oct 17 2018
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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