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

 Year-end appeal: Please make a donation to the OEIS Foundation to support ongoing development and maintenance of the OEIS. We are now in our 59th year, we have over 358,000 sequences, and we’ve crossed 10,300 citations (which often say “discovered thanks to the OEIS”). Other ways to Give
 Hints (Greetings from The On-Line Encyclopedia of Integer Sequences!)
 A130729 Fermat numbers of order 3 or F(n,3) = 2^(2^n)+3. 4
 5, 7, 19, 259, 65539, 4294967299, 18446744073709551619, 340282366920938463463374607431768211459, 115792089237316195423570985008687907853269984665640564039457584007913129639939 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,1 COMMENTS This is equivalent to F(n)+2 or 2^(2^n)+ 1 + 2. Conjecture: If n is odd, 7 is a divisor of F(n,3). The conjecture is true: the order of 2 mod 7 is 3, and if n is odd then 2^n == 2 mod 3 so 2^(2^n) + 3 == 2^2 + 3 == 0 mod 7. - Robert Israel, Nov 20 2014 LINKS Vincenzo Librandi, Table of n, a(n) for n = 0..11 Tigran Hakobyan, On the unboundedness of common divisors of distinct terms of the sequence a(n)=2^2^n+d for d>1, arXiv:1601.04946 [math.NT], 2016. FORMULA F(n,m): The n-th Fermat number of order m = 2^(2^n)+ m. The traditional Fermat numbers are F(n,1) or Fermat numbers of order 1. MATHEMATICA Table[(2^(2^n) + 3), {n, 0, 15}] (* Vincenzo Librandi, Jan 09 2013 *) PROG (PARI) fplusm(n, m)= { local(x, y); for(x=0, n, y=2^(2^x)+m; print1(y", ") ) } (Magma) [2^(2^n) + 3: n in [0..11]]; // Vincenzo Librandi, Jan 09 2013 CROSSREFS Cf. A063486, A130730. Sequence in context: A280150 A062654 A231865 * A222411 A274022 A117321 Adjacent sequences: A130726 A130727 A130728 * A130730 A130731 A130732 KEYWORD nonn AUTHOR Cino Hilliard, Jul 05 2007 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 December 3 13:06 EST 2022. Contains 358524 sequences. (Running on oeis4.)