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Search: id:A007534
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| A007534 |
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Even numbers which are not the sum of a pair of twin primes.
(Formerly M1306)
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+0
6
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| 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; listen)
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OFFSET
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1,1
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COMMENT
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No other n < 10^9. - T. D. Noe (noe(AT)sspectra.com), Apr 10 2007
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REFERENCES
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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.
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LINKS
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Eric Weisstein's World of Mathematics, Link to a section of The World of Mathematics.
Index entries for sequences related to Goldbach conjecture
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EXAMPLE
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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.
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MATHEMATICA
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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} ] ] ] ]
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CROSSREFS
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Cf. A051345.
Cf. A129363 (number of partitions of 2n into the sum of two twin primes).
Sequence in context: A009277 A018410 A156496 this_sequence A009379 A092918 A018428
Adjacent sequences: A007531 A007532 A007533 this_sequence A007535 A007536 A007537
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KEYWORD
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nonn,nice,fini
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AUTHOR
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N. J. A. Sloane (njas(AT)research.att.com), Robert G. Wilson v (rgwv(AT)rgwv.com)
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EXTENSIONS
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Conjectured to be complete (although if this were proved it would prove the "twin primes conjecture"!).
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