A131699 - OEIS

%I #13 Feb 22 2019 01:49:33

%S 1,15,322,167,6444,32183,7306,225418,6551032,683405939,7074698775,

%T 26331754107,844494314469,11303028458639,251188643150958,

%U 93364101391902,16114920282762613,239390020079624346,191165654339590395

%N Smallest number whose n-th power begins with precisely n identical digits (in base ten).

%C Main diagonal of array A[k,n] = n-th positive integer whose square (base 10) begins with k identical digits. M. F. Hasler points out that numbers whose squares start with 4 identical digits; numbers whose squares start with 5 identical digits; and numbers whose squares start with 6 identical digits; are already in the OEIS (along with A119511, A119998).

%C For the less stringent condition of the n-th power beginning with at least n identical digits, replace the numbers at indices {14,23,27,49,53} with:

%C 14 1247955519394

%C 23 2237770493401064693452

%C 27 119060799886319434107761934

%C 49 1389495494373137637129985217353011622113046714491

%C 53 6489094571807720876517179893325894917102663447322282, respectively.

%H Hans Havermann, <a href="/A131699/b131699.txt">Table of n, a(n) for n=1..100</a>

%F a(n) = Min{k>0 such that k^n begins with precisely n identical leftmost digits (base ten)}.

%e a(1) = 1 because 1^1 = 1 begins with precisely 1 identical digit.

%e a(2) = 15 because 15^2 = 225 begins with precisely 2 identical digits.

%e a(3) = 322 because 322^3 = 33386248 begins with precisely 3 identical digits.

%e a(4) = 167 because 167^4 = 777796321 begins with precisely 4 identical digits.

%e a(5) = 6444 because 6444^5 = 11111627111310388224 begins with precisely 5 identical digits.

%Y See A132392 for another version.

%Y Cf. A119511, A119998, A131573.

%K base,nonn

%O 1,2

%A _Jonathan Vos Post_ and _Hans Havermann_, Sep 15 2007

%E Edited by _N. J. A. Sloane_, Jul 01 2008 at the suggestion of _R. J. Mathar_