cp's OEIS Frontend

The first 20 terms correspond to n from 0 to 19, which makes 11*n^2 + 55*n + 43 a prime-generating polynomial (see the link).

There are only a few prime-generating quadratic polynomials whose coefficients contain at most two digits that produce 20 or more primes in a row. This is one of them, others include A005846, A007641, A060844, and A007637.

First 29 values are primes.

From Peter Bala, Apr 18 2018: (Start)

Let P(n) = 6*n^2 + 6*n + 31. The polynomial P(2*n-14) = 24*n^2 - 660*n + 4567 takes distinct prime values for n = 0 to 28.

The value of the polynomial 2*P(3/2*(n-10)) = 27*n^2 - 522*n + 2582 for n = 0 to 22 is either double a prime or a prime (alternately).

The value of the polynomial 4*P(4/3*(n-9)) = 32*n^2 - 552*n + 2469 for n = 0 to 28 is either prime or 3 times a prime, except when n = 16. (End)

Also, numbers k such that 2*k/3 - 2/3 - 19 is a perfect square. - Bruno Berselli, Apr 23 2018

Equivalently, numbers k such that 6*k - 177 is a square. - Vincenzo Librandi, Apr 23 2018