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A224505
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Primes p such that p+1 is the sum of the squares of a pair of twin primes.
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1
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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
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OFFSET
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1,1
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COMMENTS
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Obviously, no prime has the form q^2+(q+2)^2+1, where q and q+2 are twin primes.
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LINKS
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EXAMPLE
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3529 (prime) is in the sequence because 3529+1 = 41^2+43^2, where 41 and 43 are twin primes.
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MAPLE
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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;
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MATHEMATICA
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Select[(#[[1]]^2 + #[[2]]^2 - 1) & /@ Select[Partition[Prime[Range[700]], 2, 1], #[[2]] - #[[1]] == 2 &], PrimeQ]
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PROG
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(Magma) [p: r in PrimesUpTo(5000) | IsPrime(r+2) and IsPrime(p) where p is 2*r^2+4*r+3];
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CROSSREFS
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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.
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KEYWORD
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nonn
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AUTHOR
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STATUS
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approved
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