OFFSET
1,1
COMMENTS
Superset of A081767, as proved by Luke Pebody. Terms not in A081767 include 3, 7, 127, 511, ... - Ralf Stephan, Oct 12 2004
Equivalently, numbers k such that binomial(2k-3,k-1) == 0 (mod k*(k-1)/2), or: binomial(2k-2,k-1) == 0 (mod k^2-k), or: the Catalan number A000108(k-1) is divisible by k-1, i.e., a(n) = A014847(n) + 1. Indeed, 2(2k-3)!/(k!*(k-1)!) = 2(2k-2)!/(k!(k-1)!(2k-2)) = C(k-1)/(k-1). - M. F. Hasler, Nov 11 2015
LINKS
Vincenzo Librandi, Table of n, a(n) for n = 1..1000
FORMULA
a(n) = A014847(n) + 1. - Enrique Pérez Herrero, Feb 03 2013
MATHEMATICA
Select[Range[500], IntegerQ[2 (2 # - 3)!/(#! (# - 1)!)] &] (* Arkadiusz Wesolowski, Sep 06 2011 *)
PROG
(PARI) for(n=2, 999, binomial(2*n-2, n-1)%(n^2-n)||print1(n", "))
(PARI) is_A004782(n)=!binomod(2*n-2, n-1, n^2-n) \\ Using http://home.gwu.edu/~maxal/gpscripts/binomod.gp by M. Alekseyev. - M. F. Hasler, Nov 11 2015
KEYWORD
nonn
AUTHOR
EXTENSIONS
Offset corrected and initial term added by Arkadiusz Wesolowski, Sep 06 2011
STATUS
approved