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

Author

Zhining Yang, Feb 21 2024

Keywords

• nonn
• base
• changed

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.

Examples

			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).
		

Links

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

Crossrefs

Cf. A004159, A067179, A348300, A348303.

Programs

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}]

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)])

Extensions

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