This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A260349 #13 Jul 06 2020 05:59:39
%S A260349 1,3,7,17,55,59,19,167,31,311,289,227,351,203,379,197,103,1253,829,
%T A260349 335,211,353,649,437,1921,1853,2869,917,361,263,283,1637,1213,3353,
%U A260349 1519,797,241,1691,259,1391,2503,1109,3859,1857
%N A260349 a(n) = min(k : A046067((k+1)/2) = n).
%C A260349 a(n) is the first odd number k for which k * 2^i + 1 is prime when i = n but composite for all i: 0 <= i < n, or 0 if no such k exists. Thus it is the first k for which A046067((k+1)/2) = n, and therefore also the first k for which you need to test the primality of exactly n values to show that it is not a Sierpiński number.
%C A260349 Jaeschke shows that for each n>0, the set {k : A046067((k+1)/2) = n} is infinite. - _Jeppe Stig Nielsen_, Jul 06 2020
%H A260349 Hugo van der Sanden, <a href="/A260349/b260349.txt">Table of n, a(n) for n = 0..3253</a>
%H A260349 G. Jaeschke, <a href="http://www.jstor.org/stable/2007382">On the Smallest k Such that All k*2^N + 1 are Composite</a>, Mathematics of Computation, Vol. 40, No. 161 (Jan., 1983), pp. 381-384.
%e A260349 7 * 2^i + 1 is composite for i < 2 (with values 8, 15) but prime for i = 2 (29); the smaller odd numbers 1, 3 and 5 each yield a prime for smaller i, so a(2) = 7.
%o A260349 (PARI) a(n)=forstep(k=1,+oo,2,for(i=0,n-1,ispseudoprime(k<<i+1)&&next(2));ispseudoprime(k<<n+1)&&return(k)) \\ _Jeppe Stig Nielsen_, Jul 06 2020
%Y A260349 Cf. A046067, A076336, A260350.
%K A260349 nonn
%O A260349 0,2
%A A260349 _Hugo van der Sanden_, Jul 23 2015