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

1,1

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

Links

Robert Price, Table of n, a(n) for n = 1..3530

Eric Weisstein's World of Mathematics, Prime-Generating Polynomials

Example

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

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[#] &]

Prog

(PARI) lista(nn) = for(n=0, nn, if(ispseudoprime(p=abs(7*n^2-371*n+4871)), print1(p, ", "))); \\ Altug Alkan, Apr 19 2016
(GAP) Filtered(List([0..10^2], n->7*n^2-371*n+4871), IsPrime); # Muniru A Asiru, Feb 04 2018

Crossrefs

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

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

Sequence in context: A321978 A147697 A208629 * A259329 A200972 A053396

Adjacent sequences: A272074 A272075 A272076 * A272078 A272079 A272080

Keyword

nonn

Author

Robert Price, Apr 19 2016

Status

approved