A271058 Least m such that n equals a sum of binomial coefficients C(m,k1)+C(m,k2)+C(m,k3)+... with 0<=k1

1, 1, 2, 2, 3, 3, 3, 3, 4, 4, 4, 4, 6, 4, 4, 4, 5, 8, 9, 5, 5, 5, 6, 11, 5, 5, 5, 6, 6, 5, 5, 5, 6, 6, 6, 6, 6, 6, 19, 19, 6, 6, 6, 6, 8, 8, 6, 6, 6, 6, 6, 6, 26, 9, 9, 6, 6, 6, 29, 29, 30, 6, 6, 6, 7, 8, 10, 11, 34, 7, 7, 7, 8, 8, 37, 37, 7, 7, 7, 8, 9, 9, 9, 7, 7, 7, 8, 8

Offset: 1

Author

Logan J. Kleinwaks, Mar 29 2016

Keywords

• nonn

Examples

			a(3) = 2 since 3 = C(2,0) + C(2,1) but 3 != C(1,0) or C(1,1) or C(1,0) + C(1,1).
		

Links

• Giovanni Resta, Table of n, a(n) for n = 1..2000

Programs

Mathematica

nn = 22; s = Table[Union@ Map[Total, Binomial[m, #]] &@ Rest@ Subsets@ Range[0, m], {m, nn}]; Table[SelectFirst[Range[If[n == 1, 1, Ceiling@ Log2@ n], nn], MemberQ[s[[#]], n] &], {n, 52}] /. m_ /; MissingQ@ m -> 0 (* Michael De Vlieger, Mar 30 2016, Version 10.2, values of m greater than nn show as "0". *)