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A023200
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Primes p such that p + 4 is also prime.
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89
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3, 7, 13, 19, 37, 43, 67, 79, 97, 103, 109, 127, 163, 193, 223, 229, 277, 307, 313, 349, 379, 397, 439, 457, 463, 487, 499, 613, 643, 673, 739, 757, 769, 823, 853, 859, 877, 883, 907, 937, 967, 1009, 1087, 1093, 1213, 1279, 1297, 1303, 1423, 1429, 1447, 1483
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OFFSET
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1,1
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COMMENTS
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Smaller member p of cousin prime pairs (p, p+4).
A015913 contains the composite number 305635357, so is different from the present sequence and A029710 (305635357 is the only composite member of A015913 < 10^9) - Jud McCranie, Jan 07, 2001.
Apart from the first term, all terms are of the form 6n+1.
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LINKS
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T. D. Noe, Table of n, a(n) for n = 1..10000
A. Granville and G. Martin, Prime number races
H. J. Weber, A Sieve for Cousin Primes, arXiv:1204.3795v1 [math.NT], Apr 17, 2012.
Eric Weisstein's World of Mathematics, Cousin Primes
Eric Weisstein's World of Mathematics, Twin Primes
Index entries for primes, gaps between
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FORMULA
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a(n) = A046132(n) - 4 = A087679(n) - 2.
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MAPLE
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A023200 := proc(n) option remember; if n = 1 then 3; else p := nextprime(procname(n-1)) ; while not isprime(p+4) do p := nextprime(p) ; end do: p ; end if; end proc: # R. J. Mathar, Sep 03 2011
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MATHEMATICA
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Select[Range[10^2], PrimeQ[ # ]&&PrimeQ[ #+4] &] (from Vladimir Joseph Stephan Orlovsky, Apr 29 2008)
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PROG
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(PARI) print1(3); p=7; forprime(q=11, 1e3, if(q-p==4, print1(", "p)); p=q) \\ Charles R Greathouse IV, Mar 20 2013
(MAGMA) [p: p in PrimesUpTo(1500) | NextPrime(p)-p eq 4]; // Bruno Berselli, Apr 09 2013
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CROSSREFS
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Essentially the same as A029710.
Cf. A000010, A003557, A007947, A046132, A098429.
Sequence in context: A216518 A154650 A015913 * A046136 A098044 A217035
Adjacent sequences: A023197 A023198 A023199 * A023201 A023202 A023203
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KEYWORD
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nonn
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AUTHOR
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David W. Wilson
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EXTENSIONS
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Definition revised by N. J. A. Sloane, Mar 05 2010
Definition modified by Vincenzo Librandi, Aug 02 2009
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STATUS
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approved
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