A370522 a(n) is the least n-digit number whose square has the maximum sum of digits (A348300(n)).

7, 83, 836, 8937, 94863, 987917, 9893887, 99477133, 994927133, 9380293167, 99497231067, 926174913167, 9892825177313, 89324067192437, 943291047332683, 9949874270443813, 83066231922477313, 707106074079263583, 9429681807356492126, 94180040294109027313, 888142995231510436417, 8882505274864168010583

Offset

1,1

Comments

a(n) is the last n-digit term in A067179.

As the last two of the only nine known numbers whose square has a digit mean above 8.25 (see A164841), there is a high probability that a(30)=314610537013606681884298837387 and a(31)=9984988582817657883693383344833.

Links

Zhining Yang, Table of n, a(n) for n = 1..24 (terms 11..24 from Zhao Hui Du)

Example

a(3) = 836 because among all 3-digit numbers, 836 is the smallest whose square 698896 has the maximum sum of digits, 46 = A348300(3).

Mathematica

A348300={13, 31, 46, 63, 81, 97, 112, 130, 148, 162, 180};
A370522[n_]:=Do[If[Total@IntegerDigits[k^2]==A348300[[n]], Return[k]; ], {k, 10^(n-1), 10^n-1}];
Table[A370522[n], {n, 8}]

Prog

(Python)
def A370522(n):
    A348300=[0, 13, 31, 46, 63, 81, 97, 112, 130, 148, 162, 180]
    for k in range(10**(n-1), 10**n):
        if sum(int(d) for d in str(k**2))==A348300[n]:
            return(k)
print([A370522(n) for n in range(1, 9)])

Crossrefs

Cf. A004159, A067179, A348300, A348303.

Sequence in context: A297716 A075137 A268704 * A099668 A348303 A240170

Adjacent sequences: A370519 A370520 A370521 * A370523 A370524 A370525

Keyword

nonn,base

Author

Zhining Yang, Feb 21 2024

Extensions

a(11)-a(24) from Zhao Hui Du, Feb 23 2024

Status

approved