

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

AndreiLucian Dragoi, Table of n, a(n) for n = 1..771
AndreiLucian Dragoi, Program
AndreiLucian Dragoi, The "Vertical" (generalization of) the Binary Goldbach's conjecture (VBGC 1.5e) as applied on "iterative" primes with (recursive) prime indexes (iprimeths) (the conjecture only), ResearchGate, 2017.


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 FrÃ¶hlich, Jul 06 2018


CROSSREFS

Cf. A000040, A006450.
Sequence arising from the same metaconjecture: A282251.
Sequence in context: A002491 A045958 A076067 * A065385 A244052 A324059
Adjacent sequences: A316457 A316458 A316459 * A316461 A316462 A316463


KEYWORD

nonn


AUTHOR

AndreiLucian Dragoi, Jul 04 2018


STATUS

approved



