A260349 a(n) = min(k : A046067((k+1)/2) = n).

1, 3, 7, 17, 55, 59, 19, 167, 31, 311, 289, 227, 351, 203, 379, 197, 103, 1253, 829, 335, 211, 353, 649, 437, 1921, 1853, 2869, 917, 361, 263, 283, 1637, 1213, 3353, 1519, 797, 241, 1691, 259, 1391, 2503, 1109, 3859, 1857

Offset: 0

Author

Hugo van der Sanden, Jul 23 2015

Keywords

• nonn

Comments

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.

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

Examples

			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.
		

Links

• Hugo van der Sanden, Table of n, a(n) for n = 0..3253
• G. Jaeschke, On the Smallest k Such that All k*2^N + 1 are Composite, Mathematics of Computation, Vol. 40, No. 161 (Jan., 1983), pp. 381-384.

Crossrefs

Cf. A046067, A076336, A260350.

Programs

PARI

a(n)=forstep(k=1,+oo,2,for(i=0,n-1,ispseudoprime(k<Jeppe Stig Nielsen, Jul 06 2020