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

1,2

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.

Links

Table of n, a(n) for n=1..5.

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

Sequence in context: A003191 A298272 A000438 * A321983 A219014 A341873

Adjacent sequences: A061106 A061107 A061108 * A061110 A061111 A061112

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