A260826 - OEIS

A260826

Let f(k)=2*k^2+11. For n=0,1,...,11, a(n) = smallest m >= 0 such that f(m-1) is composite if m>0, f(m), f(m+1), ...,f(m+n-1) are prime, and f(m+n) is composite.

%I #19 Feb 16 2025 08:33:26

%S 11,13,15,18,28,578,617,2067795,843755046,134239787815,1434279786435,0

%N Let f(k)=2*k^2+11. For n=0,1,...,11, a(n) = smallest m >= 0 such that f(m-1) is composite if m>0, f(m), f(m+1), ...,f(m+n-1) are prime, and f(m+n) is composite.

%C Sequence is complete, a(9) and a(10) are due to Giovanni Resta.

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

%e Note that f(0), f(1), ..., f(10) are prime, while f(11) and f(12) are composite. So a(0)=11 and a(11)=0.

%Y Cf. A050265, A092968.

%K nonn,fini,full

%O 0,1

%A _Giovanni Resta_ and _Zak Seidov_, Aug 01 2015