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

Author

Zhining Yang, Dec 27 2024

Keywords

• nonn
• base

Examples

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

Crossrefs

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

Programs

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}]

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.

Extensions

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