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Search: id:A087382
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| A087382 |
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Twin prime indices of primes forming a twin prime member. |
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+0
1
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| 3, 5, 7, 11, 13, 17, 29, 41, 43, 61, 109, 149, 179, 191, 269, 313, 347, 431, 461, 463, 601, 617, 643, 659, 829, 859, 1031, 1033, 1051, 1231, 1279, 1321, 1619, 1621, 1879, 1931, 1949, 1999, 2029, 2309, 2311, 2341, 2383, 2711, 2789, 2791, 2801, 3253, 3299, 3329
(list; graph; listen)
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OFFSET
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3,1
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COMMENT
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It is interesting that these primes occur rather frequently early on but gradually diminish as the iterations increase. Some ratios of count of twin primes p and the occurrence of prime(p) also a twin prime is as follows. Index< Ratio 1000 .74 10000 .48 100000 .39 1000000 .35 Looks like it is approaching a limit.
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EXAMPLE
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The 29th prime,109,is also a twin prime paired with the prime 107.
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PROGRAM
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(PARI) twips(n) = { c1=0; c2=0; forprime(x=3, n, if(isprime(x+2), c1++); x1=prime(x); if(isprime(x-2) || isprime(x+2), if(isprime(x1-2) || isprime(x1+2), print1(x", "); c2++; ) ) ); print(); print(c2/c1+.0) }
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CROSSREFS
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Sequence in context: A108816 A088503 A118939 this_sequence A025127 A024883 A024328
Adjacent sequences: A087379 A087380 A087381 this_sequence A087383 A087384 A087385
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KEYWORD
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easy,nonn
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AUTHOR
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Cino Hilliard (hillcino368(AT)gmail.com), Oct 21 2003
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