A292116 Numbers for which there exists a nontrivial bisection of binomial coefficients as given by Theorem 12 of Ionascu et al. (2016).

13, 14, 33, 34, 61, 62, 97, 98, 103, 141, 142, 193, 194, 253, 254, 321, 322, 397, 398, 481, 482, 573, 574, 673, 674, 713, 781, 782, 897, 898, 1021, 1022, 1153, 1154, 1293, 1294, 1441, 1442, 1597, 1598, 1761, 1762, 1933, 1934, 2113, 2114, 2301, 2302, 2497, 2498, 2701, 2702, 2913, 2914, 3133, 3134

Offset: 1

Author

N. J. A. Sloane, Sep 10 2017

Keywords

• nonn

Comments

It would be nice to have a more precise definition.

From Ray Chandler, Sep 11 2017: (Start)

The sequence is the union of three types of numbers:

(1) A060626 beginning with the 2nd term.

(2) A089508 beginning with the 3rd term and omitting even values (every third term).

(3) A082109 beginning with the 2nd term.

Note that there appear to be other solutions that are not covered by Theorem 12.

(End)

Links

• Ray Chandler, Table of n, a(n) for n = 1..10000
• Eugen J. Ionascu, Thor Martinsen, and Pantelimon Stanica, Bisecting binomial coefficients, arXiv:1610.02063 [math.CO], 2016. See p. 18.

Crossrefs

Cf. A060626, A082109, A089508.

Programs

Mathematica

lim=3000; a0={};
k=4; While[c=k^2-3;c<=lim,a0=Join[a0,{c,c+1}];k+=2];
k=2; While[c=Fibonacci[2k]*Fibonacci[2k+1]-1;c<=lim,If[OddQ[c],AppendTo[a0,c]];k++];
a0=Sort[a0] (* Ray Chandler, Sep 11 2017 *)