A243260 - OEIS

%I #16 Jul 02 2014 17:15:48

%S 81,90,99,171,180,189,261,270,279,351,360,369,441,450,459,531,540,549,

%T 621,630,639,711,720,729,801,810,819,1071,1080,1089,1161,1170,1179,

%U 1251,1260,1269,1341,1350,1359,1431,1440,1449,1521,1530,1539,1611,1620,1629

%N Numbers n such that n appears in the sequence x(i) = x(i-1) +/- digitsum(x(i-1)), where even digit sums are subtracted, odd digit sums are added and x(0) = n.

%C The auxiliary sequence begins with x(0) = n and continues by adding or subtracting the digit sum. When the digitsum(x(i-1)) is even, x(i) = x(i-1) - digitsum(x(i-1)), otherwise x(i) = x(i-1) + digitsum(x(i-1)).

%H Anthony Sand, <a href="/A243260/b243260.txt">Table of n, a(n) for n = 1..1000</a>

%F x(i) = x(i-1) + digitsum(x(i-1)) * -(1 - (digitsum(x(i-1)) mod 2) * 2).

%e digitsum(81) = 9, 9 is odd, so 81 + 9 = 90. 90 + 9 = 99. digitsum(99) = 18, 18 is even, so 99 - 18 = 81, so 81 is in the list.

%e 90 + 9 = 99. 99 - 18 = 81. 81 + 9 = 90.

%e 99 - 18 = 81. 81 + 9 = 90. 90 + 9 = 99.

%e 171 + 9 = 180. 180 + 9 = 189. 189 - 18 = 171.

%e 180 + 9 = 189. 189 - 18 = 171. 171 + 9 = 180.

%e Starting with n=81, we have 81+9(odd)=90, 90+9(odd)=99, 99-18(even)=81 for the auxiliary x(i) sequence; so 81 is in the main sequence; starting with n=90 or 99 will lead to the same cycle loop, so 90, 99 are also in this sequence.

%Y Cf. A243259, A004207.

%K nonn,base

%O 1,1

%A _Anthony Sand_, Jun 02 2014