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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 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

COMMENTS

Also: squares of the form 2*s-3, where s is a semiprime, A107317. - Franklin T. Adams-Watters, 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(n-1)^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

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Last modified December 10 01:29 EST 2022. Contains 358711 sequences. (Running on oeis4.)