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A090783 a(n) can be expressed as the difference of the squares of consecutive primes in just three distinct ways.

%I A090783 #15 Aug 15 2018 22:25:47
%S A090783 1848,6888,14280,16008,19152,36120,112728,116832,129480,139080,176520,
%T A090783 190632,190968,199752,216840,236208,252120,274848,303960,314160,
%U A090783 340368,363720,435792,458280,503160,513240,686160,688680,698880,712680,721560
%N A090783 a(n) can be expressed as the difference of the squares of consecutive primes in just three distinct ways.
%H A090783 Giovanni Resta, <a href="/A090783/b090783.txt">Table of n, a(n) for n = 1..10000</a> (first 3091 terms from Robert Israel)
%e A090783 1848 = 463^2 - 461^2 = 233^2 - 229^2 = 157^2 - 151^2.
%p A090783 N:= 10^6: # to get all terms <= N
%p A090783 V:= Vector(N/4):
%p A090783 p:= 3:
%p A090783 while p < N/2 do
%p A090783   q:= p;
%p A090783   p:= nextprime(p);
%p A090783   r:= (p^2-q^2)/4;
%p A090783   if r <= N/4 then
%p A090783     V[r]:= V[r]+1
%p A090783   fi
%p A090783 od:
%p A090783 map(`*`,select(t -> V[t]=3, [$1..N/4]),4); # _Robert Israel_, Aug 13 2018
%o A090783 (PARI) is(n) = my(i=0, v=[]); forprime(p=5, n, v=[precprime(p-1), p]; if(v[2]^2-v[1]^2==n, i++)); i==3 \\ _Felix Fröhlich_, Aug 13 2018
%Y A090783 Cf. A078667, A090784, A090785, A091878.
%K A090783 nonn
%O A090783 1,1
%A A090783 _Ray G. Opao_, Feb 08 2004
%E A090783 More terms from _Ray Chandler_, Feb 11 2004