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Search: id:A118955
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| A118955 |
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Numbers of the form 2^k + prime. |
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+0
4
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| 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 17, 18, 19, 20, 21, 23, 24, 25, 27, 29, 30, 31, 32, 33, 34, 35, 37, 38, 39, 41, 42, 43, 44, 45, 47, 48, 49, 51, 53, 54, 55, 57, 59, 60, 61, 62, 63, 65, 66, 67, 68, 69, 71, 72, 73, 74, 75, 77, 79, 80, 81, 83, 84, 85, 87, 89, 90, 91, 93
(list; graph; listen)
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OFFSET
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1,1
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COMMENT
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A109925(a(n)) > 0, complement of A118954;
A118957 is a subsequence.
The lower density is at least 0.09368 (Pintz) and upper density is at most 0.49095 (Habsieger & Roblot). The density, if it exists, is called Romanov's constant. Romani conjectures that it is around 0.434. - Charles R Greathouse IV Mar 12 2008
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REFERENCES
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Laurent Habsieger and Xavier-Francois Roblot, "On integers of the form p + 2k", Acta Arithmetica 122:1 (2006), pp. 45-50.
J. Pintz, "A note on Romanov's constant", Acta Mathematica Hungarica 112:1-2 (2006), pp. 1-14.
F. Romani, "Computations concerning primes and powers of two", Calcolo 20 (1983), pp. 319-336.
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LINKS
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Charles R Greathouse IV, Home Page [in lieu of email address]
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PROGRAM
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(PARI) Romanov(n)=local(k); k=1; while(n>k, if(isprime(n-k), return(1), k=k+k)); 0 for(n=3, 100, if(Romanov(n), print1(", "n))) - Charles R Greathouse IV Mar 12 2008
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CROSSREFS
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Sequence in context: A026505 A029674 A132147 this_sequence A108473 A026447 A130231
Adjacent sequences: A118952 A118953 A118954 this_sequence A118956 A118957 A118958
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KEYWORD
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nonn
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AUTHOR
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Reinhard Zumkeller (reinhard.zumkeller(AT)gmail.com), May 07 2006
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