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

%I

%S 5,13,29,293,997,6257,11897,18773,19421,52457,73477,109597,120413,

%T 167381,192737,218233,249017,292717,333029,361237,398261,466553,

%U 502781,546137,552113,591377,635353,683933,687341,704117,737897,885517,966353,982117,1018097,1079621

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

%C Primes of the form A000040(n)^2 + A001223(n)^2.

%C Primes of the form A134735(2n-1)^2 + A134735(2n)^2.

%C Conjecture: a(n) ~ A093343(n).

%C There are 20421247 members of this sequence below 10^20. - _Charles R Greathouse IV_, Jul 29 2013

%H Charles R Greathouse IV, <a href="/A224888/b224888.txt">Table of n, a(n) for n = 1..10000</a>

%F 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 3 and 5 are consecutive primes and 3^2 + (5-3)^2 = 9 + 4 = 13 is prime, so 13 is in the sequence.

%t Select[Table[Prime[n]^2 + (Prime[n + 1] - Prime[n])^2, {n, 200}], PrimeQ] (* _Alonso del Arte_, Jul 29 2013 *)

%o (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 Cf. A093343.

%K nonn

%O 1,1

%A _Thomas Ordowski_, Jul 24 2013

%E a(5), a(9)-a(36) from _Charles R Greathouse IV_, Jul 24 2013

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Last modified July 29 05:00 EDT 2021. Contains 346340 sequences. (Running on oeis4.)