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A103739
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Primes which are half the sum of 2 squares of primes.
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12
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17, 29, 37, 73, 89, 97, 109, 149, 157, 193, 229, 241, 269, 277, 349, 409, 433, 541, 601, 661, 709, 769, 829, 853, 929, 937, 1009, 1021, 1069, 1109, 1117, 1129, 1249, 1321, 1409, 1429, 1489, 1549, 1609, 1669, 1753, 1789, 1801, 1873, 2029, 2089, 2161, 2221
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OFFSET
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1,1
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COMMENTS
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Primes of the form x^2 + y^2, where x > y > 0, such that x-y = p and x+y = q are primes. Proof: (p^2+q^2)/2 = ((x-y)^2+(x+y)^2)/2 = x^2+y^2 so we have x = (p+q)/2 and y = (q-p)/2. - Thomas Ordowski, Sep 24 2012
All terms == 1 or 5 (mod 12). - Thomas Ordowski, Jun 28 2013
Or, primes in A143850. - Zak Seidov, Jun 06 2015
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LINKS
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T. D. Noe, Table of n, a(n) for n = 1..1000
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EXAMPLE
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17 is in the sequence because (3^2 + 5^2) / 2 = 17.
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MAPLE
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Primes:= select(isprime, [seq(2*i+1, i=1..400)]):
Psq:= map(`^`, Primes, 2):
M:= max(Psq):
S:= select(t -> t <= M/2 and isprime(t), {seq(seq((Psq[i]+Psq[j])/2, j=1..i-1), i=1..nops(Psq))}):
sort(convert(S, list)); # Robert Israel, Jun 08 2015
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PROG
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(PARI) list(lim)=my(v=List(), p2, t); lim\=1; if(lim<9, lim=9); forprime(p=3, sqrtint(2*lim-9), p2=p^2; forprime(q=3, min(sqrtint(2*lim-p2), p), if(isprime(t=(p2+q^2)/2), listput(v, t)))); Set(v) \\ Charles R Greathouse IV, Feb 14 2017
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CROSSREFS
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Intersection of A143850 and A000040.
Cf. A001248, A002313.
Sequence in context: A266965 A081985 A087937 * A255871 A060258 A196668
Adjacent sequences: A103736 A103737 A103738 * A103740 A103741 A103742
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KEYWORD
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easy,nonn
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AUTHOR
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Giovanni Teofilatto, Mar 28 2005
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EXTENSIONS
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Corrected and extended by Walter Nissen, Jul 19 2005
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STATUS
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approved
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