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

%I A130843 #9 Mar 16 2024 16:48:51
%S A130843 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,
%T A130843 54,60,63,66,67,71,72,74,75,78,79,80,81,90,99,105,108,114,117,123,124,
%U A130843 126,127,129,134,135,141,144,150,152,153,158,159,162,171,177,180,186
%N A130843 Numbers k for which a number m < k exists such that digitsum(binomial(k,m)) = k.
%H A130843 Harvey P. Dale, <a href="/A130843/b130843.txt">Table of n, a(n) for n = 1..1000</a>
%e A130843 k=13 --> m=4 because binomial(13,4) = 13!/(4!*9!) = 715 --> 7+1+5 = 13.
%e A130843 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.
%p A130843 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);
%t A130843 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 *)
%Y A130843 Cf. A131382, A131417, A131418.
%K A130843 easy,nonn,base
%O A130843 1,2
%A A130843 _Paolo P. Lava_ and _Giorgio Balzarotti_, Jul 20 2007