cp's OEIS Frontend

A124865 Numbers of the form p^2-q^2 with p > q prime.

%I A124865 #13 Apr 18 2024 12:51:29
%S A124865 5,16,21,24,40,45,48,72,96,112,117,120,144,160,165,168,192,240,264,
%T A124865 280,285,288,312,336,352,357,360,408,432,480,504,520,525,528,552,600,
%U A124865 648,672,720,768,792,816,832,837,840,888,912,936,952,957,960,1008,1032,1080
%N A124865 Numbers of the form p^2-q^2 with p > q prime.
%C A124865 The only prime term is a(1) = 5.
%C A124865 All odd terms are of the form p^2-4.
%C A124865 All even terms are divisible by 8.
%C A124865 Numbers of the form (p^2-q^2)/8 (p, q odd primes, p>q) are listed in A124866.
%C A124865 Elliott & Richner call these "ans numbers". - _Charles R Greathouse IV_, Feb 17 2014
%H A124865 Charles R Greathouse IV, <a href="/A124865/b124865.txt">Table of n, a(n) for n = 1..10000</a>
%H A124865 N. E. Elliott and D. Richner, <a href="http://cs.ucmo.edu/~mjms/2003.3/Norman-Richner/OctmjmsNorman-Richner.pdf">An investigation of the set of ans numbers</a>, Missouri J. of Math. Sci. 15 (2003), pp. 189-199.
%H A124865 Florian Luca, <a href="https://doi.org/10.35834/mjms/1316032973">On the densities of some subsets of integers</a>, Missouri Journal of Mathematical Sciences 19:3 (2007), pp. 167-170.
%F A124865 a(n) >> n log n, see Luca. - _Charles R Greathouse IV_, Feb 17 2014
%t A124865 With[{nn=60},Take[Union[#[[2]]^2-#[[1]]^2&/@Subsets[Prime[Range[nn]],{2}]],nn]] (* _Harvey P. Dale_, Aug 21 2015 *)
%o A124865 (PARI) is(n)=if(n%24, isprimepower(n+4)==2 || isprimepower(n+9)==2, fordiv(n/4,d, if(isprime(n/d/4+d) && isprime(n/d/4-d), return(1))); 0) \\ _Charles R Greathouse IV_, Feb 17 2014
%Y A124865 Apart from a(1), a subsequence of A177713.
%Y A124865 Cf. A045636 (numbers of the form p^2+q^2, p, q primes).
%Y A124865 Cf. A124866 (numbers of the form (p^2-q^2)/8, p, q odd primes, p>q).
%K A124865 nonn
%O A124865 1,1
%A A124865 _Alexander Adamchuk_, Nov 10 2006