A373289 Triangle read by rows: for 1 <= k <= n, T(n,k) is a number with n binary digits and binary weight k whose sum of decimal digits is least; in case of a tie, choose the least such number.

1, 2, 3, 4, 5, 7, 8, 10, 11, 15, 16, 20, 21, 30, 31, 32, 40, 41, 51, 61, 63, 64, 80, 100, 101, 110, 111, 127, 128, 130, 200, 201, 211, 221, 223, 255, 256, 320, 400, 300, 301, 311, 501, 510, 511, 512, 520, 521, 600, 601, 1000, 1001, 1011, 1021, 1023, 1024, 1040, 1030, 1100, 1101, 2000, 2001, 2010

Offset

1,2

Links

Robert Israel, Table of n, a(n) for n = 1..325 (rows 1 to 25, flattened)

Formula

T(A123384(i),A118738(i)) = 10^i.

T(m,1) = 2^(m-1).

T(m,m) = 2^m - 1.

Example

T(5,3) = 21 because 21 = 10101_2 has 5 binary digits of which 3 are 1, and it has a lower sum of decimal digits, 3, than the other numbers (19, 22, 25, 26 and 28) with 5 binary digits of which 3 are 1.
Triangle starts
   1;
   2,  3;
   4,  5,  7;
   8, 10, 11, 15;
  16, 20, 21, 30, 31;
  32, 40, 41, 51, 61, 63;

Maple

M:= proc(n, k) local i, R, m, b, r, v;
   R:= ListTools:-Reverse(map(t -> 2^(n-1)+add(2^(n-1-t[i]), i=1..k-1), combinat:-choose(n-1, k-1 )));
   m:= infinity;
   for r in R do
     v:= convert(convert(r, base, 10), `+`);
     if v < m then b:= r; m:= v fi;
   od;
   b
end proc:
for n from 1 to 12 do
  seq(M(n, k), k=1..n)
od;

Crossrefs

Cf. A000120, A007953, A118738, A123384, A371470.

Sequence in context: A066077 A219040 A305414 * A317296 A103740 A317578

Adjacent sequences: A373286 A373287 A373288 * A373290 A373291 A373292

Keyword

nonn,base,tabl

Author

Robert Israel, May 30 2024

Status

approved