A130843 Numbers k for which a number m < k exists such that digitsum(binomial(k,m)) = k.

1, 2, 3, 4, 5, 6, 7, 8, 9, 12, 13, 15, 16, 18, 21, 26, 27, 33, 36, 39, 42, 45, 48, 51, 52, 53, 54, 60, 63, 66, 67, 71, 72, 74, 75, 78, 79, 80, 81, 90, 99, 105, 108, 114, 117, 123, 124, 126, 127, 129, 134, 135, 141, 144, 150, 152, 153, 158, 159, 162, 171, 177, 180, 186

Offset: 1

Author

Paolo P. Lava and Giorgio Balzarotti, Jul 20 2007

Keywords

• easy
• nonn
• base

Examples

			k=13 --> m=4 because binomial(13,4) = 13!/(4!*9!) = 715 --> 7+1+5 = 13.
k=75 --> m=37 because binomial(75,37) = 75!/(37!*38!)=3446310324346630677300 --> 3+4+4+6+3+1+3+2+4+3+4+6+6+3+6+7+7+3 = 75.
		

Links

• Harvey P. Dale, Table of n, a(n) for n = 1..1000

Crossrefs

Cf. A131382, A131417, A131418.

Programs

Maple

P:=proc(n) local i,j,k,w; for i from 1 by 1 to n do for j from 1 to i do w:=0; k:=binomial(i,j); while k>0 do w:=w+k-(trunc(k/10)*10); k:=trunc(k/10); od; if i=w then print(i); break; fi; od; od; end: P(200);

Mathematica

sdbQ[n_]:=Module[{d=Total[IntegerDigits[#]]&/@Table[Binomial[n,m], {m,n-1}]}, MemberQ[d,n]]; Join[{1},Select[Range[200],sdbQ]] (* Harvey P. Dale, Jan 03 2013 *)