

A296063


a(n) is the smallest number (in absolute value) not yet in the sequence such that the arithmetic mean of the first n terms a(1), a(2), ..., a(n) is an integer. Preference is given to positive values of a(n); a(1)=1; 0 not allowed.


3



1, 1, 3, 3, 5, 5, 7, 7, 9, 9, 11, 11, 13, 13, 15, 15, 17, 17, 19, 19, 21, 21, 23, 23, 25, 25, 27, 27, 29, 29, 31, 31, 33, 33, 35, 35, 37, 37, 39, 39, 41, 41, 43, 43, 45, 45, 47, 47, 49, 49, 51, 51
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OFFSET

1,3


LINKS

Colin Barker, Table of n, a(n) for n = 1..1000
Index entries for linear recurrences with constant coefficients, signature (1,1,1).


FORMULA

a(n) = (1)^(n+1)*A109613(n+1).  Michel Marcus, Dec 05 2017
From Colin Barker, Mar 14 2020: (Start)
G.f.: x*(1 + x^2) / ((1  x)*(1 + x)^2).
a(n) = a(n1) + a(n2) + a(n3) for n>3.
(End)


MATHEMATICA

Array[(2 Floor[(# + 1)/2]  1) (2 Boole@ OddQ@ #  1) &, 52] (* or *)
Nest[Append[#, Block[{k = 1, s = 1}, While[Nand[FreeQ[#, s k], IntegerQ@ Mean[Append[#, s k]]], If[s == 1, s = 1, k++; s = 1]]; s k]] &, {1}, 51] (* Michael De Vlieger, Dec 12 2017 *)


PROG

(PARI) Vec(x*(1 + x^2) / ((1  x)*(1 + x)^2) + O(x^50)) \\ Colin Barker, Mar 14 2020


CROSSREFS

Cf. A193356 (partial sums), A059841 (a(n)/n), A109613.
Sequence in context: A117767 A340836 A293701 * A127630 A267458 A109613
Adjacent sequences: A296060 A296061 A296062 * A296064 A296065 A296066


KEYWORD

sign


AUTHOR

Enrique Navarrete, Dec 04 2017


STATUS

approved



