A378308 Array read by antidiagonals: For k >= 3, row k-2 consists of the numbers with no digits 0 in bases 3 to k.

1, 2, 1, 4, 2, 1, 5, 5, 2, 1, 7, 7, 7, 2, 1, 8, 13, 13, 7, 2, 1, 13, 14, 14, 13, 13, 2, 1, 14, 22, 22, 14, 22, 13, 2, 1, 16, 23, 23, 22, 23, 22, 13, 2, 1, 17, 25, 41, 23, 43, 23, 22, 13, 2, 1, 22, 26, 43, 43, 121, 43, 23, 22, 13, 2, 1, 23, 41, 121, 121, 122, 121, 43, 23, 23, 13, 2, 1, 25, 43, 122

Offset

1,2

Comments

Row k-2 consists of 1, 2 and numbers x with A270027(x) > k.

Links

Robert Israel, Table of n, a(n) for n = 1..378 (first 27 antidiagonals)

Example

Array starts
  1,   2,   4,   5,    7,    8,   13,   14,   16,   17,   22,   23, ...
  1,   2,   5,   7,   13,   14,   22,   23,   25,   26,   41,   43, ...
  1,   2,   7,  13,   14,   22,   23,   41,   43,  121,  122,  157, ...
  1,   2,   7,  13,   14,   22,   23,   43,  121,  122,  157,  158, ...
  1,   2,  13,  22,   23,   43,  121,  122,  157,  158,  214,  607, ...
  1,   2,  13,  22,   23,   43,  121,  122,  157,  158,  214,  607, ...
  1,   2,  13,  22,   23,   43,  121,  122,  157,  158,  214,  607, ...
  1,   2,  13,  22,   23,   43,  121,  122,  157,  158,  214,  619, ...
  1,   2,  13,  23,   43,  157,  158,  214,  619, 5471, 5557, 5561, ...
  1,   2,  13,  23,   43,  157,  158,  214,  619, 5471, 5557, 5561, ...
  1,   2,  23,  43,  157,  158,  214,  619, 5471, 5557, 5561, 5791, ...
  1,   2,  23,  43,  157,  158,  214,  619, 5471, 5791, 5821, 5822, ...
  1,   2,  23,  43,  157,  158,  214,  619, 5471, 5791, 5821, 5822, ...

Maple

g:= proc(x, d) local L, i;
  L:= convert(2^d+x, base, 2);
  add((L[i]+1)*3^(i-1), i=1..d)
end proc:
T3:= NULL:
for d from 1 to 14 do T3:= T3, seq(g(x, d), x=0..2^d-1); od:
T[3]:= [T3]:
for b from 4 to 14 do T[b]:= remove(t -> member(0, convert(t, base, b)), T[b-1]); if nops(T[b]) = 0 then printf("b=%d\n", b); break fi; od:
for b from 3 to 14 do T[b][1..14] od;

Crossrefs

Cf. A270027.

Sequence in context: A329504 A147542 A347069 * A365901 A325309 A211956

Adjacent sequences: A378305 A378306 A378307 * A378309 A378310 A378311

Keyword

nonn,tabl,base

Author

Robert Israel, Nov 22 2024

Status

approved