A372924 a(n) = (sum_digits(n^3)-n)/3.

0, 0, 2, 2, 2, 1, 1, 1, 0, 3, -3, -1, 2, 2, 1, 1, 1, 0, 0, 3, -4, -1, -1, -2, -2, -2, 0, 0, -3, -1, -7, -1, -2, -2, -5, -3, -3, -6, -4, -4, -10, -5, -5, -5, -6, -9, -6, -10, -10, -7, -14, -11, -11, -6, -9, -9, -10, -10, -13, -11, -17, -11, -12, -15, -15, -13, -10

Offset: 0

Author

Guy Harari, May 16 2024

Keywords

• sign
• base
• easy

Comments

a(n) + floor((n+1)/3) is always a multiple of 3. - Jon E. Schoenfield, May 18 2024

Examples

			For n=42, 42^3 = 74088 has sum of digits 27 so a(42) = (27 - 42)/3 = -5.
		

Crossrefs

Cf. A004164.

Programs

C

#include 
#include 
int32_t sumDigits(int64_t num)
{
  int32_t sum = 0;
  while (num > 0)
  {
    sum += num % 10;
    num /= 10;
  }
  return sum;
}
int main()
{
  for (int64_t i=0; i<10000; ++i)
  {
    int64_t num = i * i * i;
    int32_t sum = sumDigits(num);
    printf("%ld, ", (sum - i)/3);
  }
  return 0;
}

Maple

read("transforms"):
A372924 := proc(n)
    (digsum(n^3)-n)/3 ;
end proc:
seq(A372924(n),n=0..80) ; # R. J. Mathar, Jul 03 2024

Mathematica

Table[(DigitSum[n^3] - n)/3, {n, 0, 100}] (* Paolo Xausa, Jul 03 2024 *)

Formula

a(n) = (A004164(n)-n)/3.