A067442 a(1) = 1 and then smallest nontrivial n-th power starting with 1.

1, 16, 125, 16, 1024, 15625, 128, 1679616, 19683, 1024, 177147, 16777216, 1594323, 16384, 14348907, 152587890625, 131072, 101559956668416, 1162261467, 1048576, 10460353203, 17592186044416, 11920928955078125, 16777216

Offset: 1

Author

Amarnath Murthy, Feb 05 2002

Keywords

• base
• easy
• nonn

Comments

Terms from Robert G. Wilson v.

Links

• Robert Israel, Table of n, a(n) for n = 1..1007

Programs

Magma

m:=1; sol:=[1]; for n in [2..24] do k:=2; while Reverse(Intseq(k^n))[1] ne 1 do; k:=k+1;  end while; sol[m+1]:=k^n; m:=m+1; end for; sol; // Marius A. Burtea, Aug 15 2019

Maple

f:= proc(n) local x,y;
  for x from 2 to 10 do
    y:= x^n;
    if floor(y/10^ilog10(y)) = 1 then return x^n fi
  od
end proc:
f(1):= 1:
map(f, [$1..50]); # Robert Israel, Aug 13 2019

Mathematica

a = {}; Do[k = 2; While[First[IntegerDigits[k^n]] != 1, k++ ]; a = Append[a, k^n], {n, 2, 25}]; a (* Robert G. Wilson v *)

PARI

a(n) = {if (n==1, return (1)); k=2; while (! (ispower(k,n) && (digits(k)[1] == 1)), k++); k;} \\ Michel Marcus, Mar 18 2015

Python

print(1,1)
n = 1
while n < 20:
    n, p = n+1, 2
    s = str(p**n)
    while s[0] != "1":
        p = p+1
        s = str(p**n)
    print(n,p**n) # A.H.M. Smeets, Aug 16 2019