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A123232 Numbers n such that (2*n)^2 + 1 and (2*n)^2 + 3 are both prime. 1
1, 2, 5, 7, 37, 47, 65, 67, 73, 80, 115, 128, 163, 170, 175, 203, 215, 220, 235, 292, 317, 343, 350, 352, 392, 430, 460, 493, 527, 535, 578, 605, 662, 670, 677, 683, 697, 710, 728, 730, 782, 850, 892, 908, 938, 1003, 1040, 1048, 1087, 1235, 1267, 1285, 1300 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

LINKS

Harvey P. Dale, Table of n, a(n) for n = 1..1000

EXAMPLE

a(4) = 7 because 14^2 + 1 = 197 and 14^2 + 3 = 199 which are both prime.

MAPLE

for i from 1 to 1000 do if(isprime(i^2 +1) and isprime(i^2+3)) then print(i/2); end if; end do;

MATHEMATICA

Select[Range[1300], AllTrue[(2#)^2+{1, 3}, PrimeQ]&] (* The program uses the AllTrue function from Mathematica version 10 *) (* Harvey P. Dale, Jan 15 2016 *)

PROG

(MAGMA) [n: n in [0..6000] | IsPrime((2*n)^2+1)and IsPrime((2*n)^2+3)] // Vincenzo Librandi, Nov 13 2010

CROSSREFS

Cf. A001359.

Sequence in context: A160621 A028432 A019409 * A042559 A197222 A062645

Adjacent sequences:  A123229 A123230 A123231 * A123233 A123234 A123235

KEYWORD

nonn

AUTHOR

Ben Paul Thurston, Oct 06 2006

STATUS

approved

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Last modified September 24 22:46 EDT 2021. Contains 347651 sequences. (Running on oeis4.)