

A260349


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


2



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
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OFFSET

0,2


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


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. 381384.


EXAMPLE

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.


PROG

(PARI) a(n)=forstep(k=1, +oo, 2, for(i=0, n1, ispseudoprime(k<<i+1)&&next(2)); ispseudoprime(k<<n+1)&&return(k)) \\ Jeppe Stig Nielsen, Jul 06 2020


CROSSREFS

Cf. A046067, A076336, A260350.
Sequence in context: A247183 A321139 A096358 * A146147 A153758 A079634
Adjacent sequences: A260346 A260347 A260348 * A260350 A260351 A260352


KEYWORD

nonn


AUTHOR

Hugo van der Sanden, Jul 23 2015


STATUS

approved



