OFFSET
1,1
COMMENTS
This sequence shares many terms with A056637, the least prime of class n-. Note that 3^(n-1) is an upper bound for each term and the upper bound is reached for n=13 and n=14. Are all subsequent terms 3^(n-1)? The Mathematica code uses the TowerMod function in the CNT package, which is described in the book by Bressoud and Wagon. - T. D. Noe, Mar 13 2009
For n=15, n=16, and n=17, the terms are also of the form 3^(n-1), but for n=18 and n=19, the terms are prime. - Wayne VanWeerthuizen, Aug 26 2014
A185816(a(n)) = n. - Reinhard Zumkeller, Sep 02 2014
Prime terms seen up to n=20 are in eleven instances of the form j*a(n-1)+1, for j=2, 4, 6, or 12. Note, though, that a(2)=5 and a(8)=719 are exceptions to this pattern. - Wayne VanWeerthuizen, Sep 06 2014
REFERENCES
David Bressoud and Stan Wagon, A Course in Computational Number Theory, Key College Pub., 2000, p. 96.
Stan Wagon, posting to Problem of the Week mailing list, Dec 15 1997.
LINKS
D. Bressoud, CNT.m Computational Number Theory Mathematica package.
Stan Wagon, Putnam Problem Notes
Eric W. Weisstein, MathWorld: Power Tower
EXAMPLE
2^^2=2^2=4 and 2^^3=2^2^2=16. We find 4 = 16 (mod k) until k=5. So a(3)=5. - T. D. Noe, Mar 13 2009
MATHEMATICA
Needs["CNT`"]; k=1; Table[While[TowerMod[2, n, k]==TowerMod[2, n-1, k], k++ ]; k, {n, 10}] (* T. D. Noe, Mar 13 2009 *)
CROSSREFS
KEYWORD
nonn,more
AUTHOR
EXTENSIONS
Improved the name and changed the offset because I just prepended a term. - T. D. Noe, Mar 13 2009
Corrected and extended by T. D. Noe, Mar 13 2009
Terms a(15)-a(19) from Wayne VanWeerthuizen, Aug 26 2014
Terms a(20)-a(21) from Wayne VanWeerthuizen, Sep 06 2014
STATUS
approved