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Search: id:A158866
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| A158866 |
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Indices of twin primes if the sum of these twin primes+1 is an upper twin prime. |
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+0
2
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| 2, 5, 30, 31, 66, 73, 88, 91, 141, 147, 217, 513, 607, 637, 743, 760, 784, 845, 856, 911, 920, 938, 949, 958, 994, 1015, 1031, 1092, 1150, 1246, 1373, 1470, 1553, 1586, 1768, 1814, 1871, 2017, 2029, 2129, 2261, 2271, 2331, 2370, 2458, 2488, 2510, 2545, 2579
(list; graph; listen)
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OFFSET
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1,1
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COMMENT
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If the sum is a member of a twin prime pair, it always is the upper twin prime member. [Proof:
Twin primes are sequentially of the form 6n-1 and 6n+1. Then adding
according to the condition, we get 6n-1+6n+1+1 = 12n+1. This implies 12n+1 is
an upper member since if it were a lower member, 12n+1+2 would be the upper
member but 12n+3 is not prime contradicting the definition of a twin prime.
Therefore 12n+1 must be an upper twin prime member as stated.]
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FORMULA
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{k: A054735(k)+1 = A006512(j), any j} - R. J. Mathar, Apr 06 2009
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EXAMPLE
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The 30th lower twin prime is 659. 659+661+1 = 1321, prime and 1319 is too.
Then 1319 is the lower member of the twin prime pair (1319,1321). So 30 is in the sequence.
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PROGRAM
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(PARI) gp > g(n)=for(x=1, n, y=2*twinl(x)+3; if(isprime(y)&&isprime(y-2), print1(x", ")))
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CROSSREFS
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Cf. A158870.
Sequence in context: A073833 A086383 A118612 this_sequence A101078 A109739 A163800
Adjacent sequences: A158863 A158864 A158865 this_sequence A158867 A158868 A158869
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KEYWORD
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nonn
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AUTHOR
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Cino Hilliard (hillcino368(AT)hotmail.com), Mar 28 2009
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EXTENSIONS
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Edited by R. J. Mathar (mathar(AT)strw.leidenuniv.nl), Apr 06 2009
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