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A132170
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Primes of the form (3pq - q - 6)/(3p + 1), where p and q are prime.
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1
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5, 7, 11, 13, 17, 29, 37, 47, 53, 97, 101, 107, 109, 127, 137, 149, 151, 157, 179, 181, 197, 257, 263, 269, 277, 293, 307, 313, 317, 337, 347, 349, 373, 389, 397, 457, 461, 487, 509, 541, 547, 557, 569, 571, 577, 587, 599, 607, 613, 641, 643, 647, 661, 673
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OFFSET
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1,1
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COMMENTS
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5/7 q - 1 < a(n) < q and p <= (2q + 5)/3, so membership can be tested in finite time.
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LINKS
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EXAMPLE
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a(1) = (3*3*7 - 7 - 6)/(3*3 + 1) = 5.
a(2) = (3*2*11 - 11 - 6)/(3*2 + 1) = 7.
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PROG
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(PARI) /* Lists the members with q <= lim */ list(lim)=my(v=[], t); forprime(q=2, lim, forprime(p=2, (2*q+5)\3, t=q-(2*q+6)/(3*p+1); if(denominator(t)==1&&isprime(t), v=concat(v, t)))); vecsort(v, , 8)
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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