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 A270225 Lesser of twin primes where both primes are the sum of three squares. 2
 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 (list; graph; refs; listen; history; text; internal format)
 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

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Last modified April 20 22:22 EDT 2019. Contains 322310 sequences. (Running on oeis4.)