A296064 - OEIS

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A296064

a(1) = 0; thereafter 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).

0, 2, 1, -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

(list; graph; refs; listen; history; text; internal format)

OFFSET

1,2

LINKS

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

Index entries for linear recurrences with constant coefficients, signature (-1,1,1).

FORMULA

From Robert Israel, Dec 26 2017: (Start)

a(n) = a(n-3)+a(n-2)-a(n-1) for n >= 7.

G.f.: (2+3*x-4*x^2-x^3+2*x^4)*x^2/((1-x)*(x+1)^2). (End)

a(n) = 1/2+(-1)^n*(1/2-n), n>=4. - R. J. Mathar, May 14 2024

MAPLE

0, 2, 1, -3, seq(seq(s*i, s=[1, -1]), i=5..100, 2); # Robert Israel, Dec 26 2017

MATHEMATICA

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]] &, {0}, 51] (* Michael De Vlieger, Dec 12 2017 *)

CROSSREFS

Cf. A296065 (partial sums), A127630.

Essentially the same as A296063.

Sequence in context: A306977 A137655 A355621 * A167595 A328600 A179382

Adjacent sequences: A296061 A296062 A296063 * A296065 A296066 A296067

KEYWORD

sign,easy

AUTHOR

Enrique Navarrete, Dec 04 2017

STATUS

approved