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Search: id:A117876
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| A117876 |
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Primes p=prime(k) of level (1,2), i.e. such that A118534(k) = prime(k-2). |
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13
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| 23, 47, 73, 233, 353, 647, 1097, 1283, 1433, 1453, 1493, 1613, 1709, 1889, 2099, 2161, 2383, 2621, 2693, 2713, 3049, 3533, 3559, 3923, 4007, 4133, 4643, 4793, 4937, 5443, 5743, 6101, 7213, 7309, 7351, 7561, 7621, 7829, 8179, 8237, 8719, 8849, 9109, 9343
(list; graph; listen)
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OFFSET
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1,1
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COMMENT
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Let p(i) denote the i-th prime. If p(n) has level 1 in A117563, and if 2 p(n) - p(n+1) is a prime, say p(n-i), then we say that p(n) has level(1,i). Sequence gives primes of level(1,2).
The prime p(4)=7 cannot be decomposed into weight*level+gap (<=> A117563(4)=0 <=> A118534(4)=0 <=> A117078(4)=0). For all other primes, an equivalent definition would be: Primes p(n) such that 2*p(n) - p(n+1) = p(n-2). [From R. Eismann and M. F. Hasler, Nov 08 2009]
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LINKS
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Remi Eismann, Table of n, a(n) for n = 1..10000
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EXAMPLE
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29=2*23-17, 2179=2*2161-2143, 5749=2*5743-5737
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PROGRAM
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(PARI) for(n=5, 9999, 2*prime(n)-prime(n+1) == prime(n-2) & print1(prime(n), ", "))
(PARI) is_A117876(p)={ isprime(p) & isprime(d=2*p-nextprime(p+2)) & d == precprime(precprime(p-2)-2) & p>7 }
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CROSSREFS
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Cf. A117563.
Sequence in context: A140614 A001124 A139501 this_sequence A090191 A054821 A039374
Adjacent sequences: A117873 A117874 A117875 this_sequence A117877 A117878 A117879
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KEYWORD
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nonn,new
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AUTHOR
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Remi Eismann (reismann(AT)free.fr), May 02 2006
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EXTENSIONS
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Edited by N. J. A. Sloane (njas(AT)research.att.com), May 14 2006
More terms from Remi EISMANN (reismann(AT)free.fr), May 25 2006
Corrected definition, double-checked values, added PARI code M. F. Hasler (mhasler(AT)univ-ag.fr), Nov 08 2009
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