This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A033919 #27 Feb 16 2025 08:32:36
%S A033919 773,2131,2491,4471,5101,7013,8543,10711,14717,17659,19081,19249,
%T A033919 20273,21661,22193,28433,35461,37967,39079,40291,41693,48527,60443,
%U A033919 60451,60947,64133,75353,78557
%N A033919 Odd k for which k+2^m is composite for all m < k.
%C A033919 Related to the Sierpiński number problem.
%C A033919 In an archived website, Payam Samidoost gives these numbers and other results about the dual Sierpiński problem. It is conjectured that, for each of these k<78557, there is an m such that k+2^m is prime. Then a covering argument would show that 78557 is the least odd number such that 78557+2^m is composite for all m. The impediment in the "dual" problem is that it is currently very difficult to prove the primality of large numbers of the form k+2^m. It is much easier to prove the Proth primes of the form k*2^m+1 which occur in the usual Sierpiński problem. According to the distributed search project "Five or Bust", 40291 is the only value of k < 78557 for which there is currently no m known making k + 2^m a prime or probable prime. - _T. D. Noe_, Jun 14 2007 and Phil Moore (moorep(AT)lanecc.edu), Dec 14 2009
%H A033919 Mersenneforum, <a href="http://www.mersenneforum.org/forumdisplay.php?f=86">Five or Bust</a>
%H A033919 Payam Samidoost, <a href="http://web.archive.org/web/20080908010544/http://sierpinski.insider.com/dual">The dual Sierpinski problem search</a> (Archive of the site at the Wayback Machine, original link is dead)
%H A033919 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/SierpinskiNumberoftheSecondKind.html">Sierpiński Number of the Second Kind.</a>
%t A033919 t={}; Do[k=1; While[k<n && !PrimeQ[n+2^k], k++ ]; If[k==n, AppendTo[t,n]], {n,3,78557,2}]; t (* _T. D. Noe_, Jun 14 2007 *)
%Y A033919 Cf. A067760, A076336.
%K A033919 nonn
%O A033919 1,1
%A A033919 _Dan Hoey_
%E A033919 More terms from _David W. Wilson_
%E A033919 More terms from _T. D. Noe_, Jun 14 2007
%E A033919 Out-of-date information from Payam Samidoost's website corrected, using the current status on the dual Sierpiński problem from "Five or Bust," by Phil Moore (moorep(AT)lanecc.edu), Dec 14 2009
%E A033919 Broken link to Payam Samidoost's website replaced with link to archive in the Wayback Machine by _Felix Fröhlich_, Jul 11 2014
%E A033919 26213 removed from sequence following an email message from Maximilian Pacher, who reports that 2^1271+26213 is prime. - _N. J. A. Sloane_, Dec 31 2015