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A224888 Primes of the form p^2 + (q-p)^2, where p and q are consecutive primes.

%I A224888 #38 Jul 29 2013 16:14:27
%S A224888 5,13,29,293,997,6257,11897,18773,19421,52457,73477,109597,120413,
%T A224888 167381,192737,218233,249017,292717,333029,361237,398261,466553,
%U A224888 502781,546137,552113,591377,635353,683933,687341,704117,737897,885517,966353,982117,1018097,1079621
%N A224888 Primes of the form p^2 + (q-p)^2, where p and q are consecutive primes.
%C A224888 Primes of the form A000040(n)^2 + A001223(n)^2.
%C A224888 Primes of the form A134735(2n-1)^2 + A134735(2n)^2.
%C A224888 Conjecture: a(n) ~ A093343(n).
%C A224888 There are 20421247 members of this sequence below 10^20. - _Charles R Greathouse IV_, Jul 29 2013
%H A224888 Charles R Greathouse IV, <a href="/A224888/b224888.txt">Table of n, a(n) for n = 1..10000</a>
%F A224888 c(x) is O( sqrt(x/log x) / log x ), where c(x) is the counting function, the number of terms less than x.
%e A224888 3 and 5 are consecutive primes and 3^2 + (5-3)^2 = 9 + 4 = 13 is prime, so 13 is in the sequence.
%t A224888 Select[Table[Prime[n]^2 + (Prime[n + 1] - Prime[n])^2, {n, 200}], PrimeQ] (* _Alonso del Arte_, Jul 29 2013 *)
%o A224888 (PARI) p=2;forprime(q=3,1e4,if(isprime(t=p^2+(q-p)^2),print1(t", "));p=q) \\ _Charles R Greathouse IV_, Jul 24 2013
%Y A224888 Cf. A093343.
%K A224888 nonn
%O A224888 1,1
%A A224888 _Thomas Ordowski_, Jul 24 2013
%E A224888 a(5), a(9)-a(36) from _Charles R Greathouse IV_, Jul 24 2013