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Search: id:A147791
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| A147791 |
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Primes p such that p^q-2 is prime for some prime q. |
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+0
1
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| 2, 3, 5, 7, 13, 19, 29, 31, 37, 43, 47, 61, 67, 71, 89, 103, 107, 109, 127, 131, 139, 151, 163, 173, 181, 191, 199, 211, 223, 229, 233, 239, 241, 257, 271, 277, 283, 293, 313, 337, 349, 359, 367, 379, 421, 433, 439, 443, 449, 457, 467, 491, 523, 541, 547, 569
(list; graph; listen)
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OFFSET
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2,1
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COMMENT
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For p>3, p^2-1 is divisible by 6. This follows from the fact that primes p>3
are of the form 6n+1 or 6n-1 and in either case p^2-1 is divisible by 6.
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EXAMPLE
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2^2-2 = 2 prime so a(1)=2, 3^2-2= 7 prime a(2)=3. For q=2,3,5, 199^q-2 is not
prime. For q=7, 199^7-2 = 12358664279161397 prime so a(27)=199.
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PROGRAM
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(PARI) g2(n) = forprime(x=2, n, y=g(1000, x); if(y>0, print1(x", ")))
g(n, m) = p1=0; forprime(p=2, n, y=m^p-2; if(ispseudoprime(y), p1=p; break)); p1
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CROSSREFS
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Sequence in context: A134266 A062252 A153800 this_sequence A072467 A062326 A066076
Adjacent sequences: A147788 A147789 A147790 this_sequence A147792 A147793 A147794
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KEYWORD
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nonn
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AUTHOR
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Cino Hilliard (hillcino368(AT)hitmail.com), Nov 13 2008
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