1,2

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 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.

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

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

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.

See A132392 for another version.

Cf. A119511, A119998, A131573.

Sequence in context: A088913 A053102 A132392 this_sequence A077738 A068124 A094399

Adjacent sequences: A131696 A131697 A131698 this_sequence A131700 A131701 A131702

base,nonn

Jonathan Vos Post (jvospost2(AT)yahoo.com) and Hans Havermann (pxp@rogers.com), Sep 15 2007

Edited by njas, Jul 01 2008 at the suggestion of R. J. Mathar