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, 400, 406, 418, 423, 424, 436, 451, 454, 457, 469, 487, 487, 487, 513, 517, 517

Offset

1,1

Comments

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

Links

Table of n, a(n) for n=1..64.

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

Example

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

Mathematica

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

Crossrefs

Cf. A004159, A067179, A348300, A348303, A370522.

Sequence in context: A373781 A373914 A026045 * A304259 A124249 A137168

Adjacent sequences: A371725 A371726 A371727 * A371729 A371730 A371731

Keyword

nonn,base

Author

Zhining Yang, Apr 04 2024

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

Status

approved