A137715 - OEIS

%I #27 Jul 13 2023 08:37:08

%S 271129,322523,327739,482719,934909,1639459,2131043,2131099,2576089,

%T 3098059,3608251,4573999,6678713,6799831,7523281,7761437,8184977,

%U 8840599,8879993,8959163,9208337,9252323,9930469,9937637,10192733,10306187,10391933,11206501

%N Prime values of n for which n*2^k + 1 is composite for all positive integers k.

%C The sequence contains those members of A076336 that are prime.

%C Note that the terms in A076336 are presently conjectural. - _Joerg Arndt_, Jun 29 2015

%H Arkadiusz Wesolowski, <a href="/A137715/b137715.txt">Table of n, a(n) for n = 1..3670</a>

%H R. Baillie, G. Cormack, and H. C. Williams, <a href="http://dx.doi.org/10.1090/S0025-5718-1981-0616376-2">The Problem of Sierpinski Concerning k*2^n+1</a>, Mathematics of Computation, Vol. 37, No. 155 (July 1981), pp. 229-231. Corrigenda; Mathematics of Computation, Vol. 39, No. 159 (July 1982), p. 308.

%H Wilfrid Keller, <a href="http://dx.doi.org/10.1090/S0025-5718-1983-0717710-7">Factors of Fermat Numbers and Large Primes of the Form k*2^n+1</a>, Mathematics of Computation, Vol. 41, No. 164 (October 1983), pp. 661-673.

%H Mersenne Forum, <a href="http://www.mersenneforum.org/showthread.php?t=2665">The Prime Sierpinski Problem</a>.

%H Seventeen or Bust, <a href="http://www.seventeenorbust.com/">A Distributed Attack on the Sierpinski problem</a>

%H W. Sierpinski, <a href="http://gdz.sub.uni-goettingen.de/dms/resolveppn/?PPN=GDZPPN002074621">Sur un problème concernant les nombres k*2^n+1</a>, Elem. d. Math. 15, pp. 73-74, 1960.

%e As 271129 is the first known prime value of n for which n*2^k + 1 is composite for all positive integers k, a(1) = 271129.

%Y Cf. A057192, A076336, A094076.

%K nonn

%O 1,1

%A _Ant King_, Feb 09 2008

%E More terms from _Arkadiusz Wesolowski_, Apr 24 2012