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%I #67 Mar 10 2018 11:04:59
%S 4871,4507,4157,3821,3499,3191,2897,2617,2351,2099,1861,1637,1427,
%T 1231,1049,881,727,587,461,349,251,167,97,41,29,43,43,29,41,97,167,
%U 251,349,461,587,727,881,1049,1231,1427,1637,1861,2099,2351,2617,2897,3191
%N Primes of the form abs(7*k^2 - 371*k + 4871) in order of increasing nonnegative values of k.
%C For k=0 to 23, this expression generates 24 primes that decrease from 4871 to 41. It generates duplicates and the absolute value is used to avoid negative terms. The same 24 primes but in reverse order are generated in the same range of the argument by 7*k^2+49*k+41, which produces neither duplicates nor negative values and is one of relatively few quadratics with at most two-digit coefficients that generate at least 20 primes in a row. We have: 7*(n-30)^2 + 49*(n-30) + 41 = 7*n^2 - 371*n + 4871. - _Waldemar Puszkarz_, Feb 02 2018
%C See also A298078, the values of 7*n^2-7*n-43, which also contains the same 24 primes without duplicates. - _N. J. A. Sloane_, Mar 10 2018
%H Robert Price, <a href="/A272077/b272077.txt">Table of n, a(n) for n = 1..3530</a>
%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/Prime-GeneratingPolynomial.html">Prime-Generating Polynomials</a>
%e 4157 is in this sequence since 7*2^2 - 371*2 + 4871 = 28-742-4871 = 4157 is prime.
%p select(isprime, [seq(7*n^2-371*n+4871, n=0..10^2)]); # _Muniru A Asiru_, Feb 04 2018
%t n = Range[0, 100]; Select[Abs[7n^2 - 371n + 4871], PrimeQ[#] &]
%o (PARI) lista(nn) = for(n=0, nn, if(ispseudoprime(p=abs(7*n^2-371*n+4871)), print1(p, ", "))); \\ _Altug Alkan_, Apr 19 2016
%o (GAP) Filtered(List([0..10^2],n->7*n^2-371*n+4871),IsPrime); # _Muniru A Asiru_, Feb 04 2018
%Y Cf. A050268, A050267, A005846, A007641, A007635, A048988, A050265, A050266.
%Y Cf. A271980, A272074, A272075, A272076, A298078.
%K nonn
%O 1,1
%A _Robert Price_, Apr 19 2016
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