A269840 - OEIS

%I #21 Mar 17 2016 05:59:01

%S 17,41,59,107,137,179,227,281,347,419,521,569,617,641,659,809,827,857,

%T 881,1019,1049,1091,1289,1427,1451,1481,1619,1667,1697,1721,1787,1931,

%U 2027,2081,2129,2267,2339,2657,2729,2801,2969,3251,3257,3299,3329,3371,3467,3539

%N Lesser of twin primes where both are the sum of 3 nonzero squares.

%H Chai Wah Wu, <a href="/A269840/b269840.txt">Table of n, a(n) for n = 1..10000</a>

%e 17 is a term because 17 = 2^2 + 2^2 + 3^2 and 19 = 1^2 + 3^2 + 3^2.

%e 41 is a term because 41 = 3^2 + 4^2 + 4^2 and 43 = 3^2 + 3^2 + 5^2.

%e 59 is a term because 59 = 3^2 + 5^2 + 5^2 and 61 = 3^2 + 4^2 + 6^2.

%o (PARI) isA000408(n) = my(a, b) ; a=1 ; while(a^2+1<n, b=1 ; while(b<=a && a^2+b^2<n, if(issquare(n-a^2-b^2), return(1) ) ; b++ ; ) ; a++ ; ) ; return(0) ;

%o t(n,p=3) = { while( p+2 < (p=nextprime( p+1 )) || n-->0, ); p-2}

%o for(n=1, 1e2, if(isA000408(t(n)) && isA000408(t(n)+2), print1(t(n), ", ")));

%Y Cf. A000408, A001359, A085317.

%K nonn

%O 1,1

%A _Altug Alkan_, Mar 13 2016