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

1,1

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.

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 *)

Crossrefs

Cf. A060626, A082109, A089508.

Sequence in context: A042411 A167996 A308122 * A071870 A346544 A041350

Adjacent sequences: A292113 A292114 A292115 * A292117 A292118 A292119

Keyword

nonn

Author

N. J. A. Sloane, Sep 10 2017

Status

approved