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 A033919 Odd k for which k+2^m is composite for all m < k. 1
 773, 2131, 2491, 4471, 5101, 7013, 8543, 10711, 14717, 17659, 19081, 19249, 20273, 21661, 22193, 28433, 35461, 37967, 39079, 40291, 41693, 48527, 60443, 60451, 60947, 64133, 75353, 78557 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,1 COMMENTS Related to the Sierpiński number problem. 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 LINKS Mersenneforum, Five or Bust Payam Samidoost, The dual Sierpinski problem search (Archive of the site at the Wayback Machine, original link is dead) Eric Weisstein's World of Mathematics, Sierpiński Number of the Second Kind. MATHEMATICA t={}; Do[k=1; While[k

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Last modified June 16 08:46 EDT 2021. Contains 345056 sequences. (Running on oeis4.)