OFFSET
1,2
COMMENTS
Is this sequence infinite? - Charles R Greathouse IV, Sep 19 2012
From Robert Israel, Oct 05 2020:
If 10^m > ((x+1)^(1/n)-(x+1/10)^(1/n))^(-n), where x is the concatenation a(1)...a(n-1), then a(n) < 10^m.
In particular, the sequence is infinite.
a(6) has 558 digits, a(7) has 4014 digits, and a(8) has 32783 digits. (End)
REFERENCES
Amarnath Murthy, Exploring some new ideas on Smarandache type sets, functions and sequences, Smarandache Notions Journal Vol. 11, No. 1-2-3, Spring 2000.
EXAMPLE
a(1) = 1, a(1)a(2) = 16 = 4^2, a(1)a(2)a(3) = 166375 = 55^3, a(1)a(2)a(3)a(4) = 16637534623551127976881 = 359147^4.
MAPLE
ncat:= (a, b) -> a*10^(1+ilog10(b))+b:
f:= proc(n, x)
local z, d;
for d from 1 do
z:= ceil(((x+1/10)*10^d)^(1/n));
if z^n < (x+1)*10^d then return z^n - x*10^d fi
od
end proc:
R[1]:= 1: C:= 1:
for n from 2 to 6 do
R[n]:= f(n, C);
C:= ncat(C, R[n]);
od:
seq(R[i], i=1..6); # Robert Israel, Oct 05 2020
CROSSREFS
KEYWORD
base,nonn
AUTHOR
Amarnath Murthy, Apr 20 2001
EXTENSIONS
Corrected and extended by Ulrich Schimke, Feb 08 2002
Offset corrected by Robert Israel, Oct 05 2020
STATUS
approved