

A110284


Squares of the form 4p  3, where p is a prime.


8



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

1,1


COMMENTS

Also: squares of the form 2*s3, where s is a semiprime, A107317.  Franklin T. AdamsWatters, Jun 28 2010
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


LINKS

David A. Corneth, Table of n, a(n) for n = 1..16289 (First 1316 terms by Marius A. Burtea, terms < 10^11)


FORMULA

a(n) = 4*A002383(n)  3 = A088503(n1)^2.


MATHEMATICA

Select[ 4Prime[ Range[2000]]  3, IntegerQ[ Sqrt[ # ]] &] (* Robert G. Wilson v, Sep 20 2005 *)


PROG

(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


CROSSREFS

Cf. A002383, A002384, A088503, A001358.
Sequence in context: A141768 A339126 A176970 * A109367 A110588 A282631
Adjacent sequences: A110281 A110282 A110283 * A110285 A110286 A110287


KEYWORD

nonn


AUTHOR

Giovanni Teofilatto, Sep 07 2005


EXTENSIONS

Extended by Ray Chandler, Sep 07 2005


STATUS

approved



