login

Year-end appeal: Please make a donation to the OEIS Foundation to support ongoing development and maintenance of the OEIS. We are now in our 61st year, we have over 378,000 sequences, and we’ve reached 11,000 citations (which often say “discovered thanks to the OEIS”).

Primes of the form 11*n^2 + 55*n + 43.
3

%I #19 Oct 30 2017 03:42:28

%S 43,109,197,307,439,593,769,967,1187,1429,1693,1979,2287,2617,2969,

%T 3343,3739,4157,4597,5059,6577,7127,7699,8293,9547,10889,11593,14629,

%U 15443,17137,18919,19843,20789,21757,24793,25849,26927,28027,30293,32647,33857,35089

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

%C 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).

%C 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.

%H Robert Israel, <a href="/A292578/b292578.txt">Table of n, a(n) for n = 1..10000</a>

%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/Prime-GeneratingPolynomial.html">Prime-Generating Polynomial</a>

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

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

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

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

%K nonn

%O 1,1

%A _Waldemar Puszkarz_, Sep 19 2017