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A272077 Primes of the form abs(7*k^2 - 371*k + 4871) in order of increasing nonnegative values of k.

%I A272077 #68 Feb 16 2025 08:33:33
%S A272077 4871,4507,4157,3821,3499,3191,2897,2617,2351,2099,1861,1637,1427,
%T A272077 1231,1049,881,727,587,461,349,251,167,97,41,29,43,43,29,41,97,167,
%U A272077 251,349,461,587,727,881,1049,1231,1427,1637,1861,2099,2351,2617,2897,3191
%N A272077 Primes of the form abs(7*k^2 - 371*k + 4871) in order of increasing nonnegative values of k.
%C A272077 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 A272077 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 A272077 Robert Price, <a href="/A272077/b272077.txt">Table of n, a(n) for n = 1..3530</a>
%H A272077 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/Prime-GeneratingPolynomial.html">Prime-Generating Polynomials</a>
%e A272077 4157 is in this sequence since 7*2^2 - 371*2 + 4871 = 28-742-4871 = 4157 is prime.
%p A272077 select(isprime, [seq(7*n^2-371*n+4871, n=0..10^2)]); # _Muniru A Asiru_, Feb 04 2018
%t A272077 n = Range[0, 100]; Select[Abs[7n^2 - 371n + 4871], PrimeQ[#] &]
%o A272077 (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 A272077 (GAP) Filtered(List([0..10^2],n->7*n^2-371*n+4871),IsPrime); # _Muniru A Asiru_, Feb 04 2018
%Y A272077 Cf. A050268, A050267, A005846, A007641, A007635, A048988, A050265, A050266.
%Y A272077 Cf. A271980, A272074, A272075, A272076, A298078.
%K A272077 nonn
%O A272077 1,1
%A A272077 _Robert Price_, Apr 19 2016