

A316460


Even integers not of the form prime(prime(x)) + prime(prime(y)) with x > y > 0.


1



2, 4, 6, 10, 12, 18, 24, 26, 30, 32, 38, 40, 50, 54, 56, 60, 66, 68, 74, 80, 82, 92, 96, 102, 104, 106, 110, 116, 118, 122, 128, 134, 136, 146, 148, 152, 154, 156, 164, 166, 170, 172, 178, 180, 200, 204, 206, 212, 218, 226, 230, 234, 248, 254, 256, 260, 264
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OFFSET

1,1


COMMENTS

No other terms up to 10^10.
Define a 1(primeindexprime) 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(primeindexprime) as having "m" primeonprime iterations, For any m >= 0 and n >= 0, all sufficiently large even numbers are the sum of an m(primeindexprime) and an n(primeindexprime). See links.


LINKS



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, x1, if(n==prime(prime(x)) + prime(prime(y)), return(0)))); 1 \\ Felix Fröhlich, Jul 06 2018


CROSSREFS

Sequence arising from the same metaconjecture: A282251.


KEYWORD

nonn


AUTHOR



STATUS

approved



