cp's OEIS Frontend

A210578 Natural numbers that can be expressed as the sum of one or two nontrivial binomial coefficients, sorted, duplicates removed.

%I A210578 #9 Apr 27 2017 23:03:42
%S A210578 6,10,12,15,16,20,21,25,26,27,28,30,31,34,35,36,38,40,41,42,43,45,46,
%T A210578 48,49,50,51,55,56,57,60,61,62,63,64,65,66,70,71,72,73,75,76,77,78,80,
%U A210578 81,83,84,85,86,87,88,90,91,92,93,94,97,98,99,100,101,102
%N A210578 Natural numbers that can be expressed as the sum of one or two nontrivial binomial coefficients, sorted, duplicates removed.
%C A210578 Recall that the nontrivial binomial coefficients are C(n,k), 2 <= k <= n-2.
%H A210578 Robert Israel, <a href="/A210578/b210578.txt">Table of n, a(n) for n = 1..10000</a>
%e A210578 a(1) = 6, since 6 is the lowest nontrivial binomial coefficient.
%e A210578 a(2) = 10, since 10 is the lowest nontrivial binomial coefficient except 6.
%e A210578 a(3) = 12 , since 6 is the lowest nontrivial binomial coefficient and 6+6 = 12 .
%p A210578 N:= 200: # to get all terms <= N
%p A210578 BC:= {}:
%p A210578 for k from 2 do
%p A210578    if binomial(k+2,k) > N then break fi;
%p A210578    for n from k+2 do
%p A210578      v:= binomial(n,k);
%p A210578      if v > N then break fi;
%p A210578      BC:= BC union {v};
%p A210578    od;
%p A210578 od:
%p A210578 A:= BC:
%p A210578 for i from 1 to nops(BC) do
%p A210578   A:= A union select(`<=`,map(`+`,BC[1..i],BC[i]),N)
%p A210578 od:
%p A210578 sort(convert(A,list)): # _Robert Israel_, Apr 27 2017
%Y A210578 This is A006987 combined with two-term sums of members of A006987. Cf. A210577 and A007318 .
%K A210578 easy,nonn
%O A210578 1,1
%A A210578 _Douglas Latimer_, Mar 22 2012