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

 Hints (Greetings from The On-Line Encyclopedia of Integer Sequences!)
 A058220 Ultra-useful primes: smallest k such that 2^(2^n) - k is prime. 7
 1, 3, 5, 15, 5, 59, 159, 189, 569, 105, 1557, 2549, 2439, 13797, 25353, 5627, 24317, 231425, 164073 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,2 COMMENTS 2^(2^16) - 5627 was found by Joel Levy in Feb 2004. - Donovan Johnson, Sep 13 2008 Corresponding numbers to entries a(1) to a(12) are proven primes, higher terms are probable primes. - Matthias Baur, Mar 17 2020 LINKS Table of n, a(n) for n=1..19. Rosetta Code, Ultra-useful primes. FORMULA a(n) = A013603(2^n). - Jinyuan Wang, Jun 06 2020 EXAMPLE For n = 3, we see that 2^(2^3) = 2^8 = 256, which is clearly not prime. 256 - 1 = 255 = 3 * 5 * 17, so a(3) is not 1. 256 - 2 = 254 = 2 * 127, so a(3) is not 2 either. 256 - 3 = 253 = 11 * 23, so a(3) is not 3 either. 256 - 5 = 251, which is prime, so a(3) = 5. MATHEMATICA ultraUseful[n_] := Module[{x = 2^(2^n)}, x - NextPrime[x, -1]]; Array[ultraUseful, 17] (* Harvey P. Dale, Jun 04 2011 *) CROSSREFS Cf. A013603, A058221. Sequence in context: A270688 A270453 A270464 * A100181 A180620 A336882 Adjacent sequences: A058217 A058218 A058219 * A058221 A058222 A058223 KEYWORD nonn,hard,nice,more AUTHOR Warren D. Smith, Nov 30 2000 EXTENSIONS a(16)-a(17) from Donovan Johnson, Sep 13 2008 a(18) from Matthias Baur, Mar 17 2020 a(19) from Matthias Baur, Apr 04 2020 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 June 21 08:06 EDT 2024. Contains 373543 sequences. (Running on oeis4.)