A332884 a(n) = -n^2 + 21*n - 1.

19, 37, 53, 67, 79, 89, 97, 103, 107, 109, 109, 107, 103, 97, 89, 79, 67, 53, 37, 19, -1, -23, -47, -73, -101, -131, -163, -197, -233, -271, -311, -353, -397, -443, -491, -541, -593, -647, -703, -761, -821, -883, -947, -1013, -1081, -1151, -1223, -1297, -1373, -1451, -1531, -1613

Offset: 1

Author

Tamer Özsoy, Jul 02 2020

Keywords

• sign
• easy

Comments

All the positive numbers of the form -(x^2 - 21*x + 1) are primes. Compare A335984.

References

• T. Özsoy, Visualization of Prime Numbers: Twin Prime Numbers, Ozsoy Triangle and Ozsoy Series, in A. Baki, B. Güven, and M. Güler, editors, Proc. 4th International Symposium of Turkish Computer and Mathematics Education, 26-Sep 28 2019, İzmir; pages 678-688.

Links

• Index entries for linear recurrences with constant coefficients, signature (3,-3,1).

Crossrefs

Cf. A059425, A335984.

Programs

Mathematica

Table[-n^2+21n-1,{n,60}] (* or *) LinearRecurrence[{3,-3,1},{19,37,53},60] (* Harvey P. Dale, Mar 07 2023 *)

PARI

a(n)=-n^2+21*n-1 \\ Charles R Greathouse IV, Oct 21 2022

Formula

G.f.: (x^2 + 20*x - 19)/(x - 1)^3. - Jinyuan Wang, Jul 08 2020