A078683 - OEIS

%I #23 Oct 21 2024 00:03:11

%S 3,5,7,17,11,13,29,17,19,41,23,97,53,29,31,257,137,37,1217,41,43,89,

%T 47,97,101,53,109,113,59,61,7937,257,67,137,71,73,149,1217,79,641,83,

%U 337,173,89,181,11777

%N Least prime of the form n*2^m+1 for m>0, or 0 if there is no such prime.

%C The next prime has 178 digits. See A078680 for the values of m.

%H Vincenzo Librandi, <a href="/A078683/b078683.txt">Table of n, a(n) for n = 1..1000</a>

%H N. J. A. Sloane, <a href="https://www.youtube.com/watch?v=3RAYoaKMckM">A Nasty Surprise in a Sequence and Other OEIS Stories</a>, Experimental Mathematics Seminar, Rutgers University, Oct 10 2024, Youtube video; <a href="https://sites.math.rutgers.edu/~zeilberg/expmath/sloane85BD.pdf">Slides</a> [Mentions this sequence]

%t Table[m=1; While[! PrimeQ[p = n*2^m + 1], m++]; p, {n, 50}]

%o (PARI) a(n)=if(n<0, 0, m=1; while(isprime(n*2^m+1)==0, m++); n*2^m+1)

%Y Cf. A078680.

%K nonn

%O 1,1

%A _Benoit Cloitre_, Dec 17 2002

%E Edited by _T. D. Noe_, Feb 25 2011