A133445 Write numbers in ternary under each other (right justified), read diagonals in SW-NE direction, sum digits.

0, 1, 3, 1, 2, 4, 2, 4, 3, 1, 2, 4, 2, 3, 5, 3, 5, 4, 2, 3, 5, 3, 4, 6, 5, 4, 3, 1, 2, 4, 2, 3, 5, 3, 5, 4, 2, 3, 5, 3, 4, 6, 4, 6, 5, 3, 4, 6, 4, 5, 7, 6, 5, 4, 2, 3, 5, 3, 4, 6, 4, 6, 5, 3, 4, 6, 4, 5, 7, 5, 7, 6, 4, 5, 7, 5, 6, 9, 5, 4, 3, 1, 2, 4, 2, 3, 5, 3, 5, 4, 2

Offset: 1

Author

Ctibor O. Zizka, Dec 22 2007

Keywords

• nonn
• base

Comments

The digit sum of A102370 "sloping binary numbers" equals A089400. What about "sloping numbers" and their digit sums in other bases?

Examples

			Numbers written in ternary:
    0
    1
    2
   10
   11
   12
   20
   21
   22
  100
  101
  102
  .....
The NW-SE diagonals are:
  0
  1
  12
  10
  11
  22
  20
  121
  102
  ......
giving 0, 1, 3, 1, 2, 4, 2, 4, 3, 1, 2, 4, ...
		

Crossrefs

Cf. A102370.

Programs

PARI

lista(nn) = {my(v = vector(nn), nb); for (n=1, nn, v[n] = digits(n-1, 3); nb = #v[n];); for (n=1, nn, if (#v[n] < nb, v[n] = concat(vector(nb-#v[n]), v[n]));); my(list = List()); for (n=nb, nn, my(s=0, pos=1); forstep(k=n, n-nb+1, -1, s += (v[k])[pos]; pos++;); listput(list, s);); Vec(list);} \\ Michel Marcus, Mar 16 2022

Extensions

New name using formula and more terms from Michel Marcus, Mar 16 2022