A371470 Triangle read by rows: for 1 <= k <= n, T(n,k) is the least sum of decimal digits of numbers with n binary digits and binary weight k.

1, 2, 3, 4, 5, 7, 8, 1, 2, 6, 7, 2, 3, 3, 4, 5, 4, 5, 6, 7, 9, 10, 8, 1, 2, 2, 3, 10, 11, 4, 2, 3, 4, 5, 7, 12, 13, 5, 4, 3, 4, 5, 6, 6, 7, 8, 7, 8, 6, 7, 1, 2, 3, 4, 6, 7, 5, 4, 2, 3, 2, 3, 3, 4, 6, 13, 14, 6, 5, 3, 4, 4, 3, 4, 6, 7, 8, 18, 19, 5, 6, 6, 5, 6, 6, 6, 7, 8, 9, 14, 19, 20, 7, 8, 5

Offset

1,2

Links

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

Formula

a(n) = A007953(A373289(n)).

T(A123384(i),A118738(i)) = 1.

Example

T(5,3) = 3 because the numbers with 5 binary digits of which 3 are 1 are 19, 21, 22, 25, 26 and 28, and the least sum of decimal digits of these is 3 (for 21).
Triangle starts:
  1;
  2, 3;
  4, 5, 7;
  8, 1, 2, 6;
  7, 2, 3, 3, 4;
  5, 4, 5, 6, 7, 9;

Maple

M:= proc(n, k) local i, R, m, 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 m:= v fi;
   od;
   m
end proc:
for n from 1 to 12 do
  seq(M(n, k), k=1..n)
od;

Crossrefs

Cf. A000120, A007953, A118738, A123384, A373289.

Sequence in context: A214921 A265566 A265550 * A306012 A082352 A122320

Adjacent sequences: A371467 A371468 A371469 * A371471 A371472 A371473

Keyword

nonn,base,tabl

Author

Robert Israel, May 31 2024

Status

approved