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

1,1

Comments

Nontrivial binomial coefficients are C(n,k) with 2 <= k <= n-2.

Links

Charles R Greathouse IV, Table of n, a(n) for n = 1..10000

Example

a(1) = 12 since 6 is the lowest nontrivial binomial coefficient and 6+6 = 12.

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 *)

Prog

(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

Crossrefs

Two-term sums of members of A006987.

Cf. A007318.

Sequence in context: A054281 A171955 A225071 * A231903 A364405 A337703

Adjacent sequences: A210574 A210575 A210576 * A210578 A210579 A210580

Keyword

easy,nonn

Author

Douglas Latimer, Mar 22 2012

Status

approved