

A276986


Numbers n for which there is a permutation p of (1,2,3,...,n) such that k+p(k) is a Catalan number for 1<=k<=n.


1



0, 1, 3, 4, 9, 10, 12, 13, 28, 29, 31, 32, 37, 38, 40, 41, 90, 91, 93, 94, 99, 100, 102, 103, 118, 119, 121, 122, 127, 128, 130, 131, 297, 298, 300, 301, 306, 307, 309, 310, 325, 326, 328, 329, 334, 335, 337, 338, 387, 388, 390, 391, 396, 397, 399, 400, 415, 416
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OFFSET

1,3


COMMENTS

A001453 is a subsequence.  Altug Alkan, Sep 29 2016
n>=1 is in the sequence if and only if there is a Catalan number c such that c/2 <= n < c and cn1 is in the sequence.  Robert Israel, Nov 20 2016


LINKS

Robert Israel, Table of n, a(n) for n = 1..10000


FORMULA

a(i) + a(2^n+1i) = A000108(n+1)1 for 1<=i<=2^n.  Robert Israel, Nov 20 2016


EXAMPLE

3 is in the sequence because the permutation (1,3,2) added termwise to (1,2,3) yields (2,5,5) and both 2 and 5 are Catalan numbers.


MAPLE

S:= {0}:
for i from 1 to 8 do
c:= binomial(2*i, i)/(i+1);
S:= S union map(t > c  t  1, S);
od:
sort(convert(S, list)); # Robert Israel, Nov 20 2016


MATHEMATICA

CatalanTo[n0_] :=
Module[{n = n0}, k = 1; L = {};
While[CatalanNumber[k] <= 2*n, L = {L, CatalanNumber[k]}; k++];
L = Flatten[L]]
perms[n0_] := Module[{n = n0, S, func, T, T2},
func[k_] := Cases[CatalanTo[n], x_ /; 1 <= x  k <= n]  k;
T = Tuples[Table[func[k], {k, 1, n}]];
T2 = Cases[T, x_ /; Length[Union[x]] == Length[x]];
Length[T2]]
Select[Range[41], perms[#] > 0 &]


CROSSREFS

Cf. A000108, A073364.
Sequence in context: A005836 A054591 A121153 * A283984 A283985 A275893
Adjacent sequences: A276983 A276984 A276985 * A276987 A276988 A276989


KEYWORD

nonn


AUTHOR

Gary E. Davis, Sep 24 2016


EXTENSIONS

More terms from Alois P. Heinz, Sep 28 2016
a(23)a(58) from Robert Israel, Nov 18 2016


STATUS

approved



