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 A210577 Natural numbers equal to the sum of two nontrivial binomial coefficients, sorted, duplicates removed. 2
 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 (list; graph; refs; listen; history; text; internal format)
 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 A337703 A337700 Adjacent sequences:  A210574 A210575 A210576 * A210578 A210579 A210580 KEYWORD easy,nonn AUTHOR Douglas Latimer, Mar 22 2012 STATUS approved

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Last modified January 19 22:04 EST 2022. Contains 350466 sequences. (Running on oeis4.)