OFFSET
1,1
COMMENTS
No other terms up to 10^10.
Define a 1-(prime-index-prime) with index x to be a number of the form prime(prime(x)). These are the even integers that cannot be expressed as 1_P(x) + 1_P(y), with 1_P(x) != 1_P(y).
Conjecture: Define an m-(prime-index-prime) as having "m" prime-on-prime iterations, For any m >= 0 and n >= 0, all sufficiently large even numbers are the sum of an m-(prime-index-prime) and an n-(prime-index-prime). See links.
LINKS
Andrei-Lucian Dragoi, Table of n, a(n) for n = 1..771
Andrei-Lucian Dragoi, Program
EXAMPLE
6 cannot be written as a sum of pair of distinct numbers (1_P(x), 1_P(y)), as 6 = 3 + 3 is the only way to write 6 as the sum of two primes, so 6 is a term.
14 can be written as 14 = 3 + 11 with 3 = 1_P(1) and 11 = 1_P(3), so 14 is not a term.
MATHEMATICA
Complement[2 Range[(Prime[Prime[998]] + 1)/2], Sort@ Flatten@ Table[ Prime[Prime[x]] + Prime[Prime[y]], {y, 2, 998}, {x, y - 1}]] (* Robert G. Wilson v, Aug 01 2018 *)
PROG
(PARI) is(n) = if(n%2==1, return(0)); for(x=2, n, for(y=1, x-1, if(n==prime(prime(x)) + prime(prime(y)), return(0)))); 1 \\ Felix Fröhlich, Jul 06 2018
CROSSREFS
KEYWORD
nonn
AUTHOR
Andrei-Lucian Dragoi, Jul 04 2018
STATUS
approved