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A075321
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Pair the odd primes so that the k-th pair is (p, p+2k) where p is the smallest prime not included earlier such that p and p+2k are primes and p+2k also does not occur earlier: (3, 5), (7, 11), (13, 19), (23, 31), (37, 47), (17, 29), ... This is the sequence of the first member of every pair.
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3, 7, 13, 23, 37, 17, 45, 55, 43, 53, 67, 79, 83, 99, 101, 107, 115, 137, 113, 157, 169, 179, 181, 191, 201, 229, 257, 41, 235, 247, 269, 199, 167, 245, 277, 287, 243, 165, 193, 339, 285, 337, 353, 373, 389, 351, 397, 283, 401, 349, 385, 417, 435, 415, 459
(list; graph; refs; listen; history; internal format)
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OFFSET
| 1,1
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COMMENTS
| Question: Is every prime a member of some pair?
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EXAMPLE
| a(4)=23: For the 4th pair though 17 is the smallest prime not occurring earlier, 17+8 = 25 is not a prime and 23 + 8 = 31 is a prime.
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PROG
| (PARI) v=vector(10^5):for(n=1, 100, f=0:i=3:while(!f, while(v[i], i=nextprime(i+1)): if(isprime(i+2*n)&&!v[i+2*n], f=1:v[i]=1:v[i+2*n]=1:print1(i", "):break, i=i+1)))
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CROSSREFS
| Cf. A075322, A075323.
Sequence in context: A124129 A101301 A103116 * A164787 A131205 A058682
Adjacent sequences: A075318 A075319 A075320 * A075322 A075323 A075324
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KEYWORD
| nonn
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AUTHOR
| Amarnath Murthy (amarnath_murthy(AT)yahoo.com), Sep 14 2002
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EXTENSIONS
| More terms from Ralf Stephan (ralf(AT)ark.in-berlin.de), Mar 27 2003
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