A283391 - OEIS

%I #15 Mar 07 2017 11:00:03

%S 5,13,17,29,37,53,61,73,97,109,113,137,149,181,193,197,229,233,277,

%T 293,313,317,337,349,401,421,449,457,461,521,541,569,613,641,653,673,

%U 677,701,709,757,809,821,853,877,929,941,977,997,1009,1021,1049,1061,1069,1093,1117

%N Primes p such that a^2 + b^2 = p^2 and q = a + b is prime, where a,b > 0.

%C Primes p = x^2 + y^2 such that q = x^2 - y^2 + 2*x*y is prime, where x > y > 0.

%C Primes q are 7, 17, 23, 41, 47, 73, 71, 103, 137, 151, 127, 193, 191, ...

%H Charles R Greathouse IV, <a href="/A283391/b283391.txt">Table of n, a(n) for n = 1..10000</a>

%t Select[Prime@ Range@ 200, Length@ Select[PowersRepresentations[#^2, 2, 2], PrimeQ@ Total@ # &] > 1 &] (* _Michael De Vlieger_, Mar 07 2017 *)

%o (PARI) T=thueinit('x^2+1,1);

%o is(n)=if(n%4 != 1 || !isprime(n), return(0)); my(v=thue(T,n^2)); for(i=1,#v, if(v[i][1]>0 && v[i][2]>=v[i][1] && isprime(vecsum(v[i])), return(1))); 0 \\ _Charles R Greathouse IV_, Mar 07 2017

%Y Subsequence of A002144.

%K nonn

%O 1,1

%A _Thomas Ordowski_, Mar 07 2017

%E More terms from _Altug Alkan_, Mar 07 2017