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 A007534 Even numbers that are not the sum of a pair of twin primes. (Formerly M1306) 17
 2, 4, 94, 96, 98, 400, 402, 404, 514, 516, 518, 784, 786, 788, 904, 906, 908, 1114, 1116, 1118, 1144, 1146, 1148, 1264, 1266, 1268, 1354, 1356, 1358, 3244, 3246, 3248, 4204, 4206, 4208 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,1 COMMENTS Conjectured to be complete (although if this were proved it would prove the "twin primes conjecture"!). No other n < 10^9. - T. D. Noe, Apr 10 2007 Of these 35, the only 5 which are two times a prime (or in A001747) are 4 = 2 * 2, 94 = 2 * 47, 514 = 2 * 257, 1114 = 2 * 557, 1354 = 2 * 677. - Jonathan Vos Post, Mar 06 2010 REFERENCES Harvey Dubner, Twin Prime Conjectures, Journal of Recreational Mathematics, Vol. 30 (3), 1999-2000. N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence). D. Wells, The Penguin Dictionary of Curious and Interesting Numbers. Penguin Books, NY, 1986, 132. LINKS Harvey Dubner, Twin Prime Conjectures, Journal of Recreational Mathematics, Vol. 30 (3), 1999-2000. Eric Weisstein's World of Mathematics, Twin Primes Dan Zwillinger, A Goldbach Conjecture Using Twin Primes, Math. Comp. 33, No.147 (1979), p.1071. EXAMPLE The twin primes < 100 are 3, 5, 7, 11, 13, 17, 19, 29, 31, 41, 43, 59, 61, 71, 73. 94 is in the sequence because no combination of any two numbers from the set just enumerated can be summed to make 94. MATHEMATICA p = Select[ Range[ 4250 ], PrimeQ[ # ] && PrimeQ[ # + 2 ] & ]; q = Union[ Join[ p, p + 2 ] ]; Complement[ Table[ n, {n, 2, 4250, 2} ], Union[ Flatten[ Table[ q[ [ i ] ] + q[ [ j ] ], {i, 1, 223}, {j, 1, 223} ] ] ] ] Complement[Range[2, 4220, 2], Union[Total/@Tuples[Union[Flatten[ Select[ Partition[ Prime[ Range], 2, 1], #[]-#[]==2&]]], 2]]] (* Harvey P. Dale, Oct 09 2013 *) PROG (Haskell) import qualified Data.Set as Set (map, null) import Data.Set (empty, insert, intersection) a007534 n = a007534_list !! (n-1) a007534_list = f [2, 4..] empty 1 a001097_list where    f xs'@(x:xs) s m ps'@(p:ps)      | x > m = f xs' (insert p s) p ps      | Set.null (s `intersection` Set.map (x -) s) = x : f xs s m ps'      | otherwise = f xs s m ps' -- Reinhard Zumkeller, Nov 27 2011 CROSSREFS Cf. A051345. Cf. A129363 (number of partitions of 2n into the sum of two twin primes). Cf. A179825. Sequence in context: A335571 A335291 A156496 * A299784 A009379 A092918 Adjacent sequences:  A007531 A007532 A007533 * A007535 A007536 A007537 KEYWORD nonn,nice AUTHOR STATUS approved

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Last modified May 8 08:51 EDT 2021. Contains 343666 sequences. (Running on oeis4.)