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A292116
Numbers for which there exists a nontrivial bisection of binomial coefficients as given by Theorem 12 of Ionascu et al. (2016).
1
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
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
KEYWORD
nonn
AUTHOR
N. J. A. Sloane, Sep 10 2017
STATUS
approved