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Search: id:A126960
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| A126960 |
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Primes p such that (3p)^2 + 2 is prime. |
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+0
1
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| 3, 5, 7, 11, 13, 19, 37, 41, 73, 79, 83, 101, 103, 107, 139, 149, 151, 167, 191, 227, 233, 251, 269, 311, 337, 443, 457, 479, 499, 503, 521, 541, 601, 613, 647, 673, 761, 811, 829, 863, 877, 883, 887, 907, 919, 941, 983, 997
(list; graph; listen)
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OFFSET
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1,1
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COMMENT
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A generalization of this would be primes p such that (kp)^2+2 is prime. Then k=3 is the only solution. This follows from the fact that k of the form 3m+/-1 will give 9m^2+6m+1+2 a multiple of 3.
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REFERENCES
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Garath A. Jones and Mary Jones, Elementary Number Theory, Springer - Verlag London, 1998; p. 35, Exercise 2.17.
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PROGRAM
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(PARI) g(n) = forprime(x=0, n, y=9*x^2+2; if(isprime(y), print1(x", ")))
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CROSSREFS
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Sequence in context: A040993 A078425 A020587 this_sequence A119753 A040140 A066651
Adjacent sequences: A126957 A126958 A126959 this_sequence A126961 A126962 A126963
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KEYWORD
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easy,nonn
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AUTHOR
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Cino Hilliard (hillcino368(AT)hotmail.com), Mar 19 2007
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EXTENSIONS
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Entries confirmed by Zak Seidov, Mar 19 2007
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