|
|
A071705
|
|
Least k > n such that C(2n,n) divides C(2k,k).
|
|
1
|
|
|
1, 2, 5, 9, 13, 20, 18, 21, 20, 63, 50, 131, 111, 67, 197, 113, 113, 338, 335, 173, 426, 110, 110, 554, 515, 515, 368, 368, 515, 928, 928, 1269, 1152, 1152, 1269, 1511, 1462, 1456, 1458, 1458, 2524, 2181, 2895, 2895, 2895, 2805, 3379, 3379, 3640, 2808, 3284
(list;
graph;
refs;
listen;
history;
text;
internal format)
|
|
|
OFFSET
|
0,2
|
|
COMMENTS
|
Erdős proved that a(n) >= 2n, and that there is a constant c > 0 such that for sufficient large n, n^(1+c) < a(n) < (2n)^(log(n)/log(2)). - Amiram Eldar, May 18 2017
|
|
LINKS
|
|
|
MATHEMATICA
|
f[n_] := Block[{k = n + 1}, bn = Binomial[2n, n]; While[ !IntegerQ[ Binomial[2k, k]/bn], k++ ]; k]; Table[ f[n], {n, 0, 50}]
lk[n_]:=Module[{k=n+1, c=Binomial[2n, n]}, While[Mod[Binomial[2k, k], c]!=0, k++]; k]; Array[lk, 60, 0] (* Harvey P. Dale, Apr 02 2022 *)
|
|
PROG
|
(PARI) for(n=1, 45, s=n+1; while(binomial(2*s, s)%binomial(2*n, n)>0, s++); print1(s, ", "))
|
|
CROSSREFS
|
|
|
KEYWORD
|
nonn
|
|
AUTHOR
|
|
|
EXTENSIONS
|
|
|
STATUS
|
approved
|
|
|
|