A132170 - OEIS

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A132170

Primes of the form (3pq - q - 6)/(3p + 1), where p and q are prime.

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

1,1

COMMENTS

5/7 q - 1 < a(n) < q and p <= (2q + 5)/3, so membership can be tested in finite time.

LINKS

Table of n, a(n) for n=1..54.

EXAMPLE

a(1) = (3*3*7 - 7 - 6)/(3*3 + 1) = 5.

a(2) = (3*2*11 - 11 - 6)/(3*2 + 1) = 7.

PROG

(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)

CROSSREFS

Sequence in context: A346990 A038958 A109416 * A106309 A371566 A227576

Adjacent sequences: A132167 A132168 A132169 * A132171 A132172 A132173

KEYWORD

nonn

AUTHOR

Juri-Stepan Gerasimov, Aug 28 2008

EXTENSIONS

Corrected and rewritten by Charles R Greathouse IV, Mar 25 2010

STATUS

approved