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

4871, 4507, 4157, 3821, 3499, 3191, 2897, 2617, 2351, 2099, 1861, 1637, 1427, 1231, 1049, 881, 727, 587, 461, 349, 251, 167, 97, 41, 29, 43, 43, 29, 41, 97, 167, 251, 349, 461, 587, 727, 881, 1049, 1231, 1427, 1637, 1861, 2099, 2351, 2617, 2897, 3191

Offset: 1

Author

Robert Price, Apr 19 2016

Keywords

• nonn

Comments

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

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

Examples

			4157 is in this sequence since 7*2^2 - 371*2 + 4871 = 28-742-4871 = 4157 is prime.
		

Links

• Robert Price, Table of n, a(n) for n = 1..3530
• Eric Weisstein's World of Mathematics, Prime-Generating Polynomials

Crossrefs

Cf. A050268, A050267, A005846, A007641, A007635, A048988, A050265, A050266.

Cf. A271980, A272074, A272075, A272076, A298078.

Programs

GAP

Filtered(List([0..10^2],n->7*n^2-371*n+4871),IsPrime); # Muniru A Asiru, Feb 04 2018

Maple

select(isprime, [seq(7*n^2-371*n+4871, n=0..10^2)]); # Muniru A Asiru, Feb 04 2018

Mathematica

n = Range[0, 100]; Select[Abs[7n^2 - 371n + 4871], PrimeQ[#] &]

PARI

lista(nn) = for(n=0, nn, if(ispseudoprime(p=abs(7*n^2-371*n+4871)), print1(p, ", "))); \\ Altug Alkan, Apr 19 2016