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A033919 Odd k for which k+2^m is composite for all m < k. 2
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 (list; graph; refs; listen; history; text; internal format)



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


Table of n, a(n) for n=1..29.

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.


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 *)


Cf. A067760, A076336.

Sequence in context: A240843 A133963 A133964 * A055521 A255156 A233991

Adjacent sequences:  A033916 A033917 A033918 * A033920 A033921 A033922




Dan Hoey


More terms from David W. Wilson

More terms from T. D. Noe, Jun 14 2007

Out-of-date information from Payam Samidoost's website corrected, using the current status on the dual Sierpiński problem from "Five or Bust," by Phil Moore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

Broken link to Payam Samidoost's website replaced with link to archive in the Wayback Machine by Felix Fröhlich, Jul 11 2014



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Last modified November 30 18:58 EST 2015. Contains 264670 sequences.