A369953 a(n) is the least integer k such that the sum of the digits of k^2 is 9*n.

0, 3, 24, 63, 264, 1374, 3114, 8937, 60663, 94863, 545793, 1989417, 5477133, 20736417, 82395387, 260191833, 706399164, 2428989417, 9380293167, 28105157886, 99497231067, 538479339417, 1974763271886, 4472135831667, 14106593458167, 62441868958167, 244744764757083, 836594274358167

Offset: 0

Author

Zhining Yang, Feb 06 2024

Keywords

• nonn
• base

Comments

3|a(n).

Examples

			a(3)=63 because k=63 is the least integer k such that the sum of the digits of k^2 = 3969 is 9*3 = 27 (3+9+6+9 = 27).
		

Links

• Zhining Yang, Table of n, a(n) for n = 0..40 (terms 19..40 from Zhao Hui Du)
• Shouen Wang, Chinese BBS: How many of these A's are there?

Crossrefs

Cf. A004159, A008591, A067179, A369955.

Programs

Mathematica

n=1;lst={};For[k=0,k<10^8,k+=3,If[Total[IntegerDigits[k^2]]==9*n,AppendTo[lst,k];n++]];lst

PARI

a(n) = my(k=0); while(sumdigits(k^2) != 9*n, k+=3); k; \\ Michel Marcus, Feb 17 2024

Python

n=1
lst=[]
for k in range(0,10**8,3):
    if sum(int(d) for d in str(k*k))==9*n:
        lst.append(k)
        n=n+1
print(lst)

Formula

a(n) = A067179(4n).

Extensions

a(19)-a(27) from Zhao Hui Du, Feb 09 2024