A061109 a(1) = 1; a(n) = smallest number such that the concatenation a(1)a(2)...a(n) is an n-th power.

1, 6, 6375, 34623551127976881, 18860302374385155610185422853070042488899966126368559233360607121925651097253827765970857

Offset: 1

Author

Amarnath Murthy, Apr 20 2001

Keywords

• base
• nonn

Comments

Is this sequence infinite? - Charles R Greathouse IV, Sep 19 2012

From Robert Israel, Oct 05 2020: (Start)

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)

Examples

			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.
		

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.

Programs

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

Extensions

Corrected and extended by Ulrich Schimke, Feb 08 2002

Offset corrected by Robert Israel, Oct 05 2020