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Search: id:A069360
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| A069360 |
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Number of prime pairs (p,q), p <= q, such that (p+q)/2 = 2*n. |
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+0
4
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| 0, 1, 1, 2, 2, 3, 2, 2, 4, 3, 3, 5, 3, 3, 6, 5, 2, 6, 5, 4, 8, 4, 4, 7, 6, 5, 8, 7, 6, 12, 5, 3, 9, 5, 7, 11, 5, 4, 11, 8, 5, 13, 6, 7, 14, 8, 5, 11, 9, 8, 14, 7, 6, 13, 9, 7, 12, 7, 9, 18, 9, 6, 16, 8, 10, 16, 9, 7, 16, 14, 8, 17, 8, 8, 21, 10, 8, 17, 10, 11
(list; graph; listen)
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OFFSET
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1,4
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COMMENT
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a(n) = #{k | 2*n-k and 2*n+k are prime, 1<=k<=2*n};
The Goldbach conjecture, if true, would imply a(m) > 0 for m > 1.
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LINKS
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K. Brockhaus, Table of n, a(n) for n=1..10000
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EXAMPLE
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n=8: there are 16 pairs (i,j) with (i+j)/2=n*2=16; only two of them, (3,29) and (13,19), consist of primes, therefore a(8)=2.
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MATHEMATICA
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Table[ Length[ Select[ Range[ 2*n ], PrimeQ[ 2n - # ] && PrimeQ[ 2n + # ] & ] ], {n, 1, 50} ] - Stefan Steinerberger (stefan.steinerberger(AT)gmail.com), Nov 30 2007
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CROSSREFS
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Bisection of A002375.
Cf. A082467 (least k such that n-k and n+k are both primes), A134677 (records), A134678 (where records occur), A135146 (index of first occurrence of n).
Adjacent sequences: A069357 A069358 A069359 this_sequence A069361 A069362 A069363
Sequence in context: A131836 A133829 A086454 this_sequence A068050 A083900 A113517
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KEYWORD
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nonn,nice
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AUTHOR
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Reinhard Zumkeller (reinhard.zumkeller(AT)gmail.com), Apr 15 2002
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EXTENSIONS
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Edited by Klaus Brockhaus (klaus-brockhaus(AT)t-online.de), Nov 20 2007
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