A371728 a(n) is the largest number that is the digit sum of an n-digit square number.

9, 13, 19, 31, 40, 46, 54, 63, 70, 81, 88, 97, 106, 112, 121, 130, 136, 148, 154, 162, 171, 180, 187, 193, 205, 211, 220, 229, 235, 244, 253, 262, 271, 277, 286, 297, 301, 310, 319, 331, 334, 343, 355, 360, 367, 378, 388, 396

Offset: 1

Author

Zhining Yang, Apr 04 2024

Keywords

• nonn
• base
• more

Comments

a(n) appears to be approximately equal to (33*n-11)/4.

Examples

			a(6) = 46 because 46 is the largest digital sum encountered among all 6-digit squares (698896, 779689, 877969).
		

Links

• Shouen Wang, Chinese BBS: How many of these A's are there?

Crossrefs

Cf. A004159, A049415, A069665, A069666.

Cf. A056991, A348300, A379298.

Programs

Mathematica

Array[Max@Map[Total@IntegerDigits[#^2] &, Range[Floor@Sqrt[10^(#)]], Floor@Sqrt[10^(# + 1) - 1]] &, 15]

Extensions

a(22)-a(48) from Zhao Hui Du, Apr 05 2024

a(49)-a(62) from Zhining Yang, May 08 2024

a(63)-a(64) from Zhining Yang, May 23 2024

Incorrect a(61) and unverified a(49) onward deleted by Zhining Yang, Mar 03 2025