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 A103739 Primes which are half the sum of 2 squares of primes. 14
 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 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,1 COMMENTS 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 LINKS T. D. Noe, Table of n, a(n) for n = 1..1000 EXAMPLE 17 is in the sequence because (3^2 + 5^2) / 2 = 17. MAPLE 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 PROG (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 CROSSREFS Intersection of A143850 and A000040. Cf. A001248, A002313. Sequence in context: A266965 A081985 A087937 * A255871 A196668 A096785 Adjacent sequences: A103736 A103737 A103738 * A103740 A103741 A103742 KEYWORD easy,nonn AUTHOR Giovanni Teofilatto, Mar 28 2005 EXTENSIONS Corrected and extended by Walter Nissen, Jul 19 2005 STATUS approved

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Last modified February 7 13:59 EST 2023. Contains 360123 sequences. (Running on oeis4.)