A131699 Smallest number whose n-th power begins with precisely n identical digits (in base ten).

1, 15, 322, 167, 6444, 32183, 7306, 225418, 6551032, 683405939, 7074698775, 26331754107, 844494314469, 11303028458639, 251188643150958, 93364101391902, 16114920282762613, 239390020079624346, 191165654339590395

Offset: 1

Author

Jonathan Vos Post and Hans Havermann, Sep 15 2007

Keywords

• base
• nonn

Comments

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).

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:

14 1247955519394

23 2237770493401064693452

27 119060799886319434107761934

49 1389495494373137637129985217353011622113046714491

53 6489094571807720876517179893325894917102663447322282, respectively.

Examples

			a(1) = 1 because 1^1 = 1 begins with precisely 1 identical digit.
a(2) = 15 because 15^2 = 225 begins with precisely 2 identical digits.
a(3) = 322 because 322^3 = 33386248 begins with precisely 3 identical digits.
a(4) = 167 because 167^4 = 777796321 begins with precisely 4 identical digits.
a(5) = 6444 because 6444^5 = 11111627111310388224 begins with precisely 5 identical digits.
		

Links

• Hans Havermann, Table of n, a(n) for n=1..100

Crossrefs

See A132392 for another version.

Cf. A119511, A119998, A131573.

Formula

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

Extensions

Edited by N. J. A. Sloane, Jul 01 2008 at the suggestion of R. J. Mathar