This site is supported by donations to The OEIS Foundation.

 Hints (Greetings from The On-Line Encyclopedia of Integer Sequences!)
 A174711 Composites of the form 2*n^n + 1 = A216147(n). 0
 9, 55, 513, 6251, 93313, 1647087, 33554433, 774840979, 20000000001, 570623341223, 605750213184507, 22224013651116033, 875787780761718751, 36893488147419103233, 1654480523772673528355, 3956839311320627178247959 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,1 COMMENTS If p = n+2 is prime, then p divides 2*n^n + 1. Proof : Let p = n+2 prime. According to the Fermat's theorem, then n^(p-1) ==1 (mod p). Because p-1 = n+1, then n^(n+1) ==1 (mod p), and with n=p-2 ==-2 (mod p), we obtain successively : n*n^n ==1 (mod p), -2*n^n ==1 (mod p), 2*n^n == -1 (mod p) => p divides 2*n^n + 1 REFERENCES T.M. Apostol, Introduction to Analytic Number Theory, Springer-Verlag, 1976 J.M. De Koninck, A. Mercier, 1001 problemes en theorie classique des nombres, Ellipses 2004, p.52 G. H. Hardy and E. M. Wright, An Introduction to the Theory of Numbers. 3rd ed., Oxford Univ. Press, 1954, p. 2. LINKS C. K. Caldwell, Composite Numbers EXAMPLE a(2) = 9 = 3^2, a(3) = 55 = 5*11, a(4) = 513 = 3 ^ 3 * 19 MAPLE with(numtheory):for n from 0 to 50 do: x:=2*n^n + 1 : if type(x, prime)=false then print (x):else fi:od: CROSSREFS Complement of A216148 in A216147. - M. F. Hasler, Sep 02 2012 Sequence in context: A183805 A037578 A096191 * A041148 A114026 A212150 Adjacent sequences:  A174708 A174709 A174710 * A174712 A174713 A174714 KEYWORD nonn AUTHOR Michel Lagneau, Mar 27 2010 STATUS approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Transforms | Puzzles | Hot | Classics
Recent Additions | More pages | Superseeker | Maintained by The OEIS Foundation Inc.

Content is available under The OEIS End-User License Agreement .