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

1,3

Comments

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

Links

Table of n, a(n) for n=1..91.

Example

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, ...

Prog

(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

Crossrefs

Cf. A102370.

Sequence in context: A201673 A343764 A117905 * A139457 A209301 A049992

Adjacent sequences: A133442 A133443 A133444 * A133446 A133447 A133448

Keyword

nonn,base

Author

Ctibor O. Zizka, Dec 22 2007

Extensions

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

Status

approved