A369955 a(n) is the least integer m such that the sum of the digits of m^2 is 9*(k+n) where k is the number of digits of m.

3, 63, 3114, 8937, 94863, 5477133, 82395381, 706399164, 9380293167, 99497231067, 4472135831667, 62441868958167, 836594274358167, 9983486364492063, 435866837461509417, 707106074079263583, 77453069648658793167, 754718284918279954614, 8882505274864168010583

Offset

0,1

Comments

3|a(n).

Links

Table of n, a(n) for n=0..18.

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

Example

a(2)=3114 because 3114 is the least 4-digit integer whose square has digit sum 9*(4+2) = 9*6 = 54: 3114^2 = 9696996 and 9+6+9+6+9+9+6 = 54.

Mathematica

n=0; For[k=0, k<10^8/3, k++, If[Total[IntegerDigits[9k^2]]==9*(n+Ceiling@Log10@(3k)), Print[{n, 3k}]; n++]]

Prog

(Python)
def sd(n):
    return sum(int(d) for d in str(n*n))
n=0
for k in range(0, 10**8, 3):
    if sd(k)==9*(len(str(k))+n):
        print([n, k])
        n+=1
(PARI) a(n) = my(m=1); while (sumdigits(m^2) != 9*(#Str(m)+n), m++); m; \\ Michel Marcus, Feb 10 2024

Crossrefs

Cf. A004159, A067179, A369953.

Sequence in context: A133275 A258657 A331012 * A123687 A159605 A180761

Adjacent sequences: A369952 A369953 A369954 * A369956 A369957 A369958

Keyword

nonn,base

Author

Zhining Yang, Feb 06 2024

Extensions

a(9)-a(18) from Zhao Hui Du, Feb 19 2024

Status

approved