A143850 Numbers of the form (p^2 + q^2)/2, for odd primes p and q.

9, 17, 25, 29, 37, 49, 65, 73, 85, 89, 97, 109, 121, 145, 149, 157, 169, 185, 193, 205, 229, 241, 265, 269, 277, 289, 325, 349, 361, 409, 425, 433, 445, 481, 485, 493, 505, 529, 541, 565, 601, 625, 661, 685, 689, 697, 709, 745, 769, 829, 841, 845, 853, 865

Offset: 1

Author

T. D. Noe, Sep 03 2008

Keywords

• nonn

Comments

The primes in this sequence are listed in A103739.

a(n) mod 4 = 1. See A227697 for related sequence. - Richard R. Forberg, Sep 22 2013

The squares of primes in this sequence form the subsequence A001248 \ {4}. - Bernard Schott, Jul 09 2022

Links

• T. D. Noe, Table of n, a(n) for n = 1..1000

Crossrefs

Cf. A001248, A045636, A103739, A227697.

Cf. A075892 (a subsequence).

Programs

Mathematica

Take[Union[Total[#]/2&/@(Tuples[Prime[Range[2,20]],2]^2)],60] (* Harvey P. Dale, Dec 28 2014 *)

PARI

list(lim)=my(v=List(), p2); lim\=1; if(lim<9, lim=8); forprime(p=3, sqrtint(2*lim-9), p2=p^2; forprime(q=3, min(sqrtint(2*lim-p2), p), listput(v, (p2+q^2)/2))); Set(v) \\ Charles R Greathouse IV, Feb 14 2017