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%I A224505 #14 Sep 08 2022 08:46:04
%S A224505 73,1801,3529,10369,20809,103969,115201,426889,649801,2080801,2205001,
%T A224505 2654209,3266569,3328201,4428289,5171329,10017289,10672201,11347849,
%U A224505 14709889,21780001,22177801,28395649,29675809,30701449,32320801,35583049,40176649,41368609
%N A224505 Primes p such that p+1 is the sum of the squares of a pair of twin primes.
%C A224505 Primes in A184417.
%C A224505 Obviously, no prime has the form q^2+(q+2)^2+1, where q and q+2 are twin primes.
%H A224505 Bruno Berselli, <a href="/A224505/b224505.txt">Table of n, a(n) for n = 1..1000</a>
%e A224505 3529 (prime) is in the sequence because 3529+1 = 41^2+43^2, where 41 and 43 are twin primes.
%p A224505 A224505:=proc(q) local a,n;
%p A224505 for n from 1 to q do
%p A224505   if ithprime(n+1)-ithprime(n)=2 then a:=ithprime(n+1)^2+ithprime(n)^2-1;
%p A224505   if isprime(a) then print(a); fi; fi;
%p A224505 od; end: A224505(10^6); # _Paolo P. Lava_, Apr 17 2013
%t A224505 Select[(#[[1]]^2 + #[[2]]^2 - 1) & /@ Select[Partition[Prime[Range[700]], 2, 1], #[[2]] - #[[1]] == 2 &], PrimeQ]
%o A224505 (Magma) [p: r in PrimesUpTo(5000) | IsPrime(r+2) and IsPrime(p) where p is 2*r^2+4*r+3];
%Y A224505 Cf. A063533 (sums of the squares of a pair of twin primes), A118072 (primes which are sum of a pair of twin primes minus 1), A184417.
%K A224505 nonn
%O A224505 1,1
%A A224505 _Bruno Berselli_, Apr 08 2013

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