%I #13 Jul 06 2020 05:59:39

%S 1,3,7,17,55,59,19,167,31,311,289,227,351,203,379,197,103,1253,829,

%T 335,211,353,649,437,1921,1853,2869,917,361,263,283,1637,1213,3353,

%U 1519,797,241,1691,259,1391,2503,1109,3859,1857

%N a(n) = min(k : A046067((k+1)/2) = n).

%C 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 Jaeschke shows that for each n>0, the set {k : A046067((k+1)/2) = n} is infinite. - _Jeppe Stig Nielsen_, Jul 06 2020

%H Hugo van der Sanden, <a href="/A260349/b260349.txt">Table of n, a(n) for n = 0..3253</a>

%H 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 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 (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 Cf. A046067, A076336, A260350.

%K nonn

%O 0,2

%A _Hugo van der Sanden_, Jul 23 2015