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%I #16 Oct 29 2017 13:47:34
%S 31,47,79,127,191,271,367,479,607,751,911,1087,1279,1487,1951,2207,
%T 2767,3391,3727,4079,4447,4831,5231,5647,6079,6991,9007,9551,10111,
%U 10687,11279,11887,12511,13151,13807,14479,17327,20431,21247,22079,24671,26479,27407
%N Primes of the form 8*n^2+8*n+31.
%C The first 14 terms correspond to n from 0 to 13, which makes 8*n^2+8*n+31 a prime-generating polynomial (see the link).
%C This is a prime-generating polynomial of the form c*n^2+c*n+p, where c=2^k (k=0,1,2...) and p is prime with c and p containing at most two digits. Prime-generating polynomials of this kind arise for k=0,1,2,3 - see A005846 and A007635 (k=0), A007639 (k=1), and A048988 (k=2).
%C All terms are of the form 4m+3. Terms 1 and 4 are Mersenne primes (A000668).
%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/Prime-GeneratingPolynomial.html">Prime-Generating Polynomial</a>
%e 79 is a term as it is a prime corresponding to n=2: 8*4+8*2+31=79.
%t Select[Range[0,100]//8#^2+8#+31&, PrimeQ]
%o (PARI) for(n=0, 100, isprime(p=8*n^2+8*n+31)&& print1(p ", "))
%Y Cf. A000040 (primes), A005846, A007635, A007639, A048988, A281437, A292578 (similar prime-generating sequences).
%K nonn
%O 1,1
%A _Waldemar Puszkarz_, Oct 06 2017
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