A224505 Primes p such that p+1 is the sum of the squares of a pair of twin primes.

73, 1801, 3529, 10369, 20809, 103969, 115201, 426889, 649801, 2080801, 2205001, 2654209, 3266569, 3328201, 4428289, 5171329, 10017289, 10672201, 11347849, 14709889, 21780001, 22177801, 28395649, 29675809, 30701449, 32320801, 35583049, 40176649, 41368609

Offset: 1

Author

Bruno Berselli, Apr 08 2013

Keywords

• nonn

Comments

Primes in A184417.

Obviously, no prime has the form q^2+(q+2)^2+1, where q and q+2 are twin primes.

Examples

			3529 (prime) is in the sequence because 3529+1 = 41^2+43^2, where 41 and 43 are twin primes.
		

Links

• Bruno Berselli, Table of n, a(n) for n = 1..1000

Crossrefs

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.

Programs

Magma

[p: r in PrimesUpTo(5000) | IsPrime(r+2) and IsPrime(p) where p is 2*r^2+4*r+3];

Maple

A224505:=proc(q) local a,n;
for n from 1 to q do
  if ithprime(n+1)-ithprime(n)=2 then a:=ithprime(n+1)^2+ithprime(n)^2-1;
  if isprime(a) then print(a); fi; fi;
od; end: A224505(10^6); # Paolo P. Lava, Apr 17 2013

Mathematica

Select[(#[[1]]^2 + #[[2]]^2 - 1) & /@ Select[Partition[Prime[Range[700]], 2, 1], #[[2]] - #[[1]] == 2 &], PrimeQ]