A292578 Primes of the form 11*n^2 + 55*n + 43.

43, 109, 197, 307, 439, 593, 769, 967, 1187, 1429, 1693, 1979, 2287, 2617, 2969, 3343, 3739, 4157, 4597, 5059, 6577, 7127, 7699, 8293, 9547, 10889, 11593, 14629, 15443, 17137, 18919, 19843, 20789, 21757, 24793, 25849, 26927, 28027, 30293, 32647, 33857, 35089

Offset: 1

Author

Waldemar Puszkarz, Sep 19 2017

Keywords

• nonn

Comments

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.

Links

• Robert Israel, Table of n, a(n) for n = 1..10000
• Eric Weisstein's World of Mathematics, Prime-Generating Polynomial

Crossrefs

Cf. A000040, A005846, A007641, A060844, A007637 (similar sequences).

Programs

Maple

select(isprime, [seq(11*n^2+55*n+43,n=0..100)]); # Robert Israel, Oct 01 2017

Mathematica

Select[Range[0,100]//11#^2+55#+43 &, PrimeQ]

PARI

for(n=0, 100, isprime(p=11*n^2+55*n+43)&& print1(p ", "))