The OEIS is supported by the many generous donors to the OEIS Foundation.

 Hints (Greetings from The On-Line Encyclopedia of Integer Sequences!)
 A123159 Conjectured smallest Sierpiński numbers of the second kind S, base b=2,3,4,5,..., where S*b^n+1 is composite for all n>=1 and gcd(S+1, b-1) = 1. 10
 78557, 125050976086, 66741, 159986, 174308, 1112646039348, 1, 2344, 9175, 1490, 521, 132, 4, 91218919470156, 2500, 278, 398, 765174, 8, 1002, 6694, 182, 30651, 262638, 221, 8, 4554, 4, 867, 6360528, 1, 1854, 6, 214018, 1886, 2604, 14, 166134, 826477, 8, 13372, 2256, 4, 53474 (list; graph; refs; listen; history; text; internal format)
 OFFSET 2,1 COMMENTS Some values with base b=2^x+1 for integers x have also been calculated - see the links. LINKS G. Jaeschke, On the smallest k such that all k * 2^n +1 are composite, Math. Comp., 40:181 (1983) 381-384. MR 84k:10006. Primeform Group, base=2^x+1. Primeform Group, base=3. Primeform Group, base=5. Carlos Rivera, Problem 36. The Liskovets-Gallot numbers, The Prime Puzzles and Problems Connection. Guido Smetrijns, Andrew J. Walker, Shane Findley, Jim Fougeron, Mikael Klasson, Robert Smith and others, Riesel/Sierpinski in base 3, digest of 43 messages in primeform Yahoo group, May 24, 2004 - Jan 7, 2007. [Cached copy] Robert Smith, David Broadhurst, Shane Findley, Sierpinski / Riesel base 2^x+1, digest of 4 messages in primeform Yahoo group, Sep 26 - Sep 27, 2004. [Cached copy] Robert Smith, Guido Smetrijns, Mikael Klasson, Riesel Sierpinski in base 5, digest of 6 messages in primeform Yahoo group, Sep 17 - Sep 18, 2004 EXAMPLE For base=3, S+1 should be coprime to 3-1 = 2, so S must be even. Find a covering set of multiplicative orders of primes base b and discover S by trial and error using the Chinese Remainder Theorem. CROSSREFS Cf. A076336. Sequence in context: A038815 A076336 A244562 * A184230 A186612 A180973 Adjacent sequences: A123156 A123157 A123158 * A123160 A123161 A123162 KEYWORD nonn AUTHOR Robert Smith (robert_smith44(AT)hotmail.com), Oct 02 2006 EXTENSIONS a(6) from Arkadiusz Wesolowski, Nov 20 2014 a(3) corrected and a(7)-a(45) from Eric Chen, Dec 16 2014 STATUS approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recents
The OEIS Community | Maintained by The OEIS Foundation Inc.

Last modified February 4 05:49 EST 2023. Contains 360046 sequences. (Running on oeis4.)