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 A266241 Integers n such that average of first n Catalan numbers (A000108) is an integer. 0
 1, 2, 12, 377, 2504, 342317 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,2 COMMENTS Integers n such that A014137(n-1) is divisible by n. Corresponding average values are 1, 1, 6875, ... LINKS EXAMPLE 1 is a term because C(0) mod 1 = 1 mod 1 = 0. 2 is a term because (C(0) + C(1)) mod 2 = (1 + 1) mod 2 = 0. 12 is a term because (C(0) + C(1) + ... + C(10) + C(11)) mod 12 = (1 + 1 + ... + 16796 + 58786) mod 12 = 0. PROG (PARI) a(n) = sum(k=0, n, (2*k)!/(k!)^2/(k+1)) % (n+1); for(n=0, 1e5, if(a(n)==0, print1(n+1", "))); (MAGMA) a:=[1]; catalan:=1; sum:=catalan; for n in [2..350000] do catalan:=(catalan*(4*n-6)) div n; sum+:=catalan; if (sum mod n) eq 0 then a[#a+1]:=n; end if; end for; a; // Jon E. Schoenfield, Dec 25 2015 CROSSREFS Cf. A000108, A014137. Sequence in context: A158261 A215956 A251182 * A012547 A009706 A012551 Adjacent sequences:  A266238 A266239 A266240 * A266242 A266243 A266244 KEYWORD nonn,more AUTHOR Altug Alkan, Dec 25 2015 EXTENSIONS a(6) from Jon E. Schoenfield, Dec 25 2015 STATUS approved

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Last modified June 29 23:00 EDT 2022. Contains 354913 sequences. (Running on oeis4.)