A379603 a(n) is the largest n-digit number whose square contains only digits greater than 5.

3, 83, 937, 9833, 98336, 998333, 9994833, 99983333, 999939437, 9999833333, 99998333336, 999998333333, 9999983333336, 99999983333333, 999999833333336, 9999999833333333, 99999998333333336, 999999998333333333, 9999999983333333336, 99999999983333333333, 999999999833333333336

Offset

1,1

Links

Table of n, a(n) for n=1..21.

Formula

Conjecture: It appears that for all n >= 5,

a(2*n) = 100^n - (5*10^n + 1)/3, and

a(2*n + 1) = 10*a(2*n) + 6.

Example

a(3) = 937 because among all 3-digit numbers, 937 is the largest whose square 877969 contains only digits greater than 5.

Mathematica

f[m_] := For[k = 10^m - 1, k > 10^(m - 1), k--, If[Min@IntegerDigits[k^2] > 5, Return[k]; ]];
Table[f[m], {m, 10}]

Crossrefs

Cf. A053972, A053974, A058471, A164778, A164772, A164773, A164841, A291631, A379602.

Sequence in context: A178001 A173811 A093166 * A389723 A111648 A013518

Adjacent sequences: A379600 A379601 A379602 * A379604 A379605 A379606

Keyword

nonn,base

Author

Zhining Yang, Dec 27 2024

Extensions

a(20)-a(21) from Jinyuan Wang, Dec 27 2024

Status

approved