A270245 Lesser of twin primes such that sum of twin prime pair is the sum of 2 nonzero squares.

3, 179, 521, 809, 1619, 1871, 2087, 2339, 3257, 3329, 4049, 4337, 4931, 5651, 5849, 6569, 6659, 6947, 7487, 8009, 8387, 8819, 8999, 10529, 10889, 11699, 12239, 14561, 15137, 16361, 16451, 16649, 17657, 17747, 19079, 19889, 19961, 20231, 20771, 20807, 21059, 22481, 22697, 23039, 23201

Offset: 1

Author

Altug Alkan, Mar 13 2016

Keywords

• nonn

Examples

			3 is a term because 3 + 5 = 2^2 + 2^2.
179 is a term because 179 + 181 = 6^2 + 18^2.
521 is a term because 521 + 523 = 12^2 + 30^2.
809 is a term because 809 + 811 = 18^2 + 36^2.
		

Crossrefs

Cf. A000404, A001359, A054735.

Programs

Mathematica

Select[Select[Prime@ Range@ 2700, PrimeQ[# + 2] &], Length[PowersRepresentations[2 # + 2, 2, 2] /. {0, } -> Nothing] > 0 &] (* _Michael De Vlieger, Mar 15 2016 *)

PARI

isA000404(n)={ for( i=1, #n=factor(n)~%4, n[1, i]==3 && n[2, i]%2 && return); n && ( vecmin(n[1, ])==1 || (n[1, 1]==2 && n[2, 1]%2))}
t(n,p=3) = {while( p+2 < (p=nextprime( p+1 )) || n-->0, ); p-2}
for(n=1, 1e3, if(isA000404(2*t(n)+2), print1(t(n), ", ")));