A073600 Least n^k with same leading decimal digit as n, k>1.

1, 256, 387420489, 4096, 59604644775390625, 60466176, 79792266297612001, 8589934592, 984770902183611232881, 100, 121, 144, 169, 196, 11390625, 1048576, 1419857, 104976, 130321, 25600000000, 278218429446951548637196401

Offset: 1

Author

Reinhard Zumkeller, Aug 04 2002

Keywords

• nonn
• base
• look

Examples

			a(4)=4096, as 4096=4^6 is the least power of 4 with initial digit =4: 4^2=16, 4^3=64, 4^4=256 and 4^5=1024; A073601(4)=6.
		

Links

• Robert Israel, Table of n, a(n) for n = 1..5995

Programs

Maple

f:= proc(n) local t,k,m;
  t:= floor(n/10^ilog10(n));
  for k from 2 do
    m:= n^k;
    if floor(m/10^ilog10(m)) = t then return m fi
  od
end proc:
map(f, [$1..100]); # Robert Israel, Apr 21 2021

Mathematica

fi[n_] := First[IntegerDigits[n]]; Table[k = 2; While[fi[x = n^k] != fi[n], k++]; x, {n, 21}] (* Jayanta Basu, Jul 02 2013 *)

Formula

a(n) = n^A073601(n);

A000030(a(n)) = A000030(n).