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

1,2

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.

Links

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

Formula

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

Example

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.

Crossrefs

See A132392 for another version.

Cf. A119511, A119998, A131573.

Sequence in context: A053102 A327556 A132392 * A077738 A068124 A094399

Adjacent sequences: A131696 A131697 A131698 * A131700 A131701 A131702

Keyword

base,nonn

Author

Jonathan Vos Post and Hans Havermann, Sep 15 2007

Extensions

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

Status

approved