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

1,2

Comments

Terms from Robert G. Wilson v.

Links

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

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 *)

Prog

(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
(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
(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

Crossrefs

Sequence in context: A125353 A126511 A231582 * A000485 A264625 A213748

Adjacent sequences: A067439 A067440 A067441 * A067443 A067444 A067445

Keyword

base,easy,nonn

Author

Amarnath Murthy, Feb 05 2002

Status

approved