OFFSET
1,1
COMMENTS
The only primes in the sequence are 3,7,31,127,... the Mersenne primes (A000668). - Zak Seidov, Dec 08 2011
Repdigits of two or more digits, interpreted in the smallest possible base. E.g., the smallest base for 222 is 3, 222 in base 3 is 26, and 26 is in the sequence. - Franklin T. Adams-Watters, Aug 11 2014
REFERENCES
R. L. Graham, D. E. Knuth and O. Patashnik, Concrete Mathematics. Addison-Wesley, Reading, MA, 2nd edition, p. 66.
LINKS
Reinhard Zumkeller, Table of n, a(n) for n = 1..10000
L. Bibiloni, P. Viader, and J. Paradis, On a Series of Goldbach and Euler, Amer. Math. Monthly, 113 (2006), pp. 206-220.
FORMULA
a(n) = A001597(n + 1) - 1.
MATHEMATICA
f[upto_] := Union[Flatten[Table[n^pwr - 1, {pwr, 2, Log[2, upto+1]}, {n, 2, (upto+1)^(1/pwr)}]]]; f[1763] (* Zak Seidov, Dec 08 2011 *)
Select[Range[2000], GCD@@FactorInteger[#][[All, 2]]>1&]-1 (* Harvey P. Dale, Jan 31 2023 *)
PROG
(Haskell)
a045542 n = a045542_list !! (n-1)
a045542_list = map (subtract 1) $ tail a001597_list
-- Reinhard Zumkeller, Jul 15 2012
(PARI) list(lim)=my(v=List()); for(e=2, logint(lim\=1, 2), for(k=2, sqrtnint(lim, e), listput(v, k^e-1))); Set(v) \\ Charles R Greathouse IV, Aug 26 2015
CROSSREFS
KEYWORD
easy,nice,nonn
AUTHOR
William M. Glasgow (billg(AT)wakely.com)
EXTENSIONS
More terms from Larry Reeves (larryr(AT)acm.org), Jun 11 2002
STATUS
approved