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

1,1

Links

Table of n, a(n) for n=1..45.

Example

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.

Mathematica

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

Prog

(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), ", ")));

Crossrefs

Cf. A000404, A001359, A054735.

Sequence in context: A198446 A216967 A217443 * A093434 A053291 A013519

Adjacent sequences: A270242 A270243 A270244 * A270246 A270247 A270248

Keyword

nonn

Author

Altug Alkan, Mar 13 2016

Status

approved