%I #34 Jun 03 2024 18:20:18
%S 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,
%T 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,
%U 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
%N 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.
%H Robert Israel, <a href="/A371470/b371470.txt">Table of n, a(n) for n = 1..325</a> (rows 1 to 25, flattened)
%F a(n) = A007953(A373289(n)).
%F T(A123384(i),A118738(i)) = 1.
%e 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).
%e Triangle starts:
%e 1;
%e 2, 3;
%e 4, 5, 7;
%e 8, 1, 2, 6;
%e 7, 2, 3, 3, 4;
%e 5, 4, 5, 6, 7, 9;
%p M:= proc(n,k) local i,R,m,r,v;
%p R:= ListTools:-Reverse(map(t -> 2^(n-1)+add(2^(n-1-t[i]),i=1..k-1), combinat:-choose(n-1,k-1 )));
%p m:= infinity;
%p for r in R do
%p v:= convert(convert(r,base,10),`+`);
%p if v < m then m:= v fi;
%p od;
%p m
%p end proc:
%p for n from 1 to 12 do
%p seq(M(n,k),k=1..n)
%p od;
%Y Cf. A000120, A007953, A118738, A123384, A373289.
%K nonn,base,tabl
%O 1,2
%A _Robert Israel_, May 31 2024