A270225 Lesser of twin primes where both primes are the sum of three squares.

3, 11, 17, 41, 59, 107, 137, 179, 227, 281, 347, 419, 521, 569, 617, 641, 659, 809, 827, 857, 881, 1019, 1049, 1091, 1289, 1427, 1451, 1481, 1619, 1667, 1697, 1721, 1787, 1931, 2027, 2081, 2129, 2267, 2339, 2657, 2729, 2801, 2969, 3251, 3257, 3299, 3329, 3371, 3467, 3539

Offset

1,1

Links

Chai Wah Wu, Table of n, a(n) for n = 1..10000

Formula

Primes p such that p == 1 or 3 mod 8 and p+2 is prime. - Chai Wah Wu, Jul 18 2016

Example

3 is a term because 3 = 1^2 + 1^2 + 1^2 and 5 = 0^2 + 1^2 + 2^2.
17 is a term because 17 = 2^2 + 2^2 + 3^2 and 19 = 1^2 + 3^2 + 3^2.
41 is a term because 41 = 3^2 + 4^2 + 4^2 and 43 = 3^2 + 3^2 + 5^2.
59 is a term because 59 = 3^2 + 5^2 + 5^2 and 61 = 3^2 + 4^2 + 6^2.

Mathematica

Select[Prime[Range[500]], MemberQ[{1, 3}, Mod[#, 8]] && PrimeQ[# + 2] &] (* Vincenzo Librandi, Jul 18 2016 *)

Prog

(PARI) isA004215(n) = my(fouri, j) ; fouri=1 ; while( n >=7*fouri, if( n % fouri ==0, j= n/fouri-7 ; if( j % 8==0, return(1) ) ; ); fouri *= 4 ; ) ; return(0);
t(n, p=3) = { while( p+2 < (p=nextprime( p+1 )) || n-->0, ); p-2}
for(n=1, 1e2, if(!isA004215(t(n)) && !isA004215(t(n)+2), print1(t(n), ", ")));
(Python)
from sympy import prime, isprime
A270225_list = [p for p in (prime(i) for i in range(2, 10**3)) if p % 8 not in {5, 7} and isprime(p+2)] # Chai Wah Wu, Jul 18 2016
(Magma) [p: p in PrimesUpTo(4000) | IsPrime(p+2) and  p mod 8 in [1, 3]]; // Vincenzo Librandi, Jul 18 2016

Crossrefs

Cf. A001359, A004215, A269840.

Sequence in context: A203162 A240084 A100567 * A262275 A176804 A078116

Adjacent sequences: A270222 A270223 A270224 * A270226 A270227 A270228

Keyword

nonn

Author

Altug Alkan, Mar 13 2016

Status

approved