cp's OEIS Frontend

This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.

A097698 Numbers k such that both 4*k^2 - 3 and 4*k^2 + 3 are primes.

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%I A097698 #27 Sep 13 2024 15:18:12
%S A097698 2,4,5,7,32,46,56,70,73,86,109,149,152,161,163,170,175,178,208,220,
%T A097698 235,254,277,280,290,313,317,326,334,343,347,352,364,368,373,385,403,
%U A097698 409,434,446,460,527,541,551,565,578,598,628,632,689,709,710,737,761,812
%N A097698 Numbers k such that both 4*k^2 - 3 and 4*k^2 + 3 are primes.
%H A097698 Harvey P. Dale, <a href="/A097698/b097698.txt">Table of n, a(n) for n = 1..1000</a>
%F A097698 a(n) = A153975(n) / 2. - _Vladimir Joseph Stephan Orlovsky_, Apr 23 2010
%t A097698 Select[Range[0,7! ],PrimeQ[ #^2-3]&&PrimeQ[ #^2+3]&]/2 (* _Vladimir Joseph Stephan Orlovsky_, Apr 23 2010 *)
%t A097698 Select[Range[1000],AllTrue[4#^2+{3,-3},PrimeQ]&] (* The program uses the AllTrue function from Mathematica version 10 *) (* _Harvey P. Dale_, Dec 08 2019 *)
%o A097698 (Magma) [n: n in [1..1000] |IsPrime(4*n^2-3) and IsPrime(4*n^2+3)]; // _Vincenzo Librandi_, Nov 16 2010
%o A097698 (PARI) is(n)=isprime(4*n^2-3) && isprime(4*n^2+3) \\ _Charles R Greathouse IV_, Sep 27 2016
%Y A097698 Cf. A083022, A097697, A153975.
%K A097698 easy,nonn
%O A097698 1,1
%A A097698 _Carl R. White_, Aug 20 2004