OFFSET
1,2
COMMENTS
Except a(1), all terms are multiples of 3.
a(n) == {3 or 15} (mod 30) for n>2.
LINKS
Amiram Eldar, Table of n, a(n) for n = 1..10000 (terms 1..3665 from K. D. Bajpai)
EXAMPLE
a(2) = 3, {3^2 + 2 = 11, 3^2 + 4 = 13 } and {3^3 + 2 = 29, 3^3 + 4 = 31} are twin prime pairs.
a(3) = 45, {45^2 + 2 = 2027, 45^2 + 4 = 2029 } and {45^3 + 2 = 91127, 45^3 + 4 = 91129} are twin prime pairs.
MATHEMATICA
Select[Range[1000000], PrimeQ[#^2 + 2] && PrimeQ[#^2 + 4] && PrimeQ[#^3 + 2] && PrimeQ[#^3 + 4] &]
PROG
(PARI) for(n=1, 100000, if(isprime(n^2+2) && isprime(n^2+4) && isprime(n^3+2) && isprime(n^3+4), print1(n, ", ")))
CROSSREFS
KEYWORD
nonn
AUTHOR
K. D. Bajpai, Mar 14 2017
STATUS
approved