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A033919
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Odd k for which k+2^m is composite for all m < k.
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2
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773, 2131, 2491, 4471, 5101, 7013, 8543, 10711, 14717, 17659, 19081, 19249, 20273, 21661, 22193, 26213, 28433, 35461, 37967, 39079, 40291, 41693, 48527, 60443, 60451, 60947, 64133, 75353, 78557
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OFFSET
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1,1
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COMMENTS
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Related to the Sierpinski number problem.
In an archived website, Payam Samidoost gives these numbers and other results about the dual Sierpinski 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 Sierpinski 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
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LINKS
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Table of n, a(n) for n=1..29.
Eric Weisstein's World of Mathematics, Sierpinski Number of the Second Kind.
Payam Samidoost, The dual Sierpinski problem search
Mersenneforum, Five or Bust
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MATHEMATICA
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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
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CROSSREFS
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Cf. A067760, A076336.
Sequence in context: A114543 A133963 A133964 * A055521 A077077 A177845
Adjacent sequences: A033916 A033917 A033918 * A033920 A033921 A033922
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KEYWORD
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nonn
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AUTHOR
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Dan Hoey (Hoey(AT)aic.nrl.navy.mil)
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EXTENSIONS
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More terms from David W. Wilson
More terms from T. D. Noe, Jun 14 2007
Corrected the out of date information from Payam Samidoost's website with the current status on the dual Sierpinski problem from "Five or Bust", by Phil Moore (moorep(AT)lanecc.edu), Dec 14 2009
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STATUS
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approved
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