OFFSET
0,4
COMMENTS
a(14) might need to be corrected if F(14) turns out to have a smaller factor than 116928085873074369829035993834596371340386703423373313. F(20) is composite, but no explicit factor is known. - Jeppe Stig Nielsen, Feb 11 2010
REFERENCES
P. Ribenboim, The Book of Prime Number Records. Springer-Verlag, NY, 2nd ed., 1989, p. 71.
H. Riesel, ``Prime numbers and computer methods for factorization,'' Progress in Mathematics, Vol. 57, Birkhauser, Boston, 1985, Chap. 4, see p. 377.
N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
LINKS
Wilfrid Keller, Prime factors k.2^n + 1 of Fermat numbers F_m
R. G. Wilson, V, Letter to N. J. A. Sloane, Aug. 1993
FORMULA
a(n) = (A093179(n) - 1)/2^(n+2) for n >= 2. - Jianing Song, Mar 02 2021
EXAMPLE
From Jianing Song, Mar 02 2021: (Start)
F(2) = 2^(2^2) + 1 = 1*2^4 + 1;
F(3) = 2^(2^3) + 1 = 5*2^5 + 1;
F(4) = 2^(2^4) + 1 = 1024*2^6 + 1;
F(5) = 2^(2^5) + 1 = (5*2^7 + 1) * (52347*2^7 + 1);
F(6) = 2^(2^6) + 1 = (1071*2^8 + 1) * (262814145745*2^8 + 1). (End)
PROG
(PARI) a(n) = if(n<2, 0, my(lim=2^(2^n-(n+2))); for(k=1, lim, my(p=k*2^(n+2)+1); if(Mod(2, p)^(2^n)==-1, return(k)))) \\ Jianing Song, Mar 02 2021
CROSSREFS
KEYWORD
hard,nonn
AUTHOR
EXTENSIONS
a(14)-a(19) added by Max Alekseyev, May 04 2010
STATUS
approved