A210577 Natural numbers equal to the sum of two nontrivial binomial coefficients, sorted, duplicates removed.
12, 16, 20, 21, 25, 26, 27, 30, 31, 34, 35, 36, 38, 40, 41, 42, 43, 45, 46, 48, 49, 50, 51, 55, 56, 57, 60, 61, 62, 63, 64, 65, 66, 70, 71, 72, 73, 75, 76, 77, 80, 81, 83, 84, 85, 86, 87, 88, 90, 91, 92, 93, 94, 97, 98, 99, 100, 101, 102, 104, 105, 106, 110
Offset: 1
Examples
a(1) = 12 since 6 is the lowest nontrivial binomial coefficient and 6+6 = 12.
Links
- Charles R Greathouse IV, Table of n, a(n) for n = 1..10000
Programs
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Mathematica
lim = 110; bc = {}; n = 4; While[c = Select[Binomial[n, Range[2, Floor[n/2]]], # <= lim &]; Length[c] > 0, bc = Join[bc, c]; n++]; bc = Sort[bc]; Select[Union[Flatten[Outer[Plus, bc, bc]]], # <= lim &] (* T. D. Noe, Mar 22 2012 *) -
PARI
list(lim)=my(v=List(), t, u=v); for(n=4, sqrtint(2*lim)+1, for(k=2, n\2, t=binomial(n, k); if(t>lim, break, listput(v, t)))); v=vecsort(Vec(v), , 8); for(i=1,#v,for(j=1,i,if(v[i]+v[j]>lim,break,listput(u,v[i]+v[j]))));vecsort(Vec(u),,8) \\ Charles R Greathouse IV, Apr 03 2012
Comments