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Numbers n such that n appears in the sequence x(i) = x(i-1) +/- digitsum(x(i-1)), where even digitsums are added, odd digitsums are subtracted and x(0) = n.
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%I #13 Jul 01 2014 20:43:30

%S 99,108,117,198,207,216,297,306,315,396,405,414,495,504,513,594,603,

%T 612,693,702,711,792,801,810,972,990,999,1008,1098,1107,1116,1197,

%U 1206,1215,1296,1305,1314,1395,1404,1413,1494,1503,1512,1593,1602,1611,1692,1701

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

%C The sequence begins with x(0) = n and continues by adding or subtracting the digitsum. 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="/A243259/b243259.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(99) = 18, 18 is even, so 99 + 18 = 117. digitsum(117) = 9, 9 is odd, so 177 - 9 = 108. 108 - 9 = 99, hence 99 belongs to sequence.

%e 108 - 9 = 99, 99 + 18 = 117, 117 - 9 = 108, hence 108 is in the sequence.

%e 117 - 9 = 108. 108 - 9 = 99. 99 + 18 = 117.

%e 198 + 18 = 216. 216 - 9 = 207. 207 - 9 = 198.

%Y Cf. A004207, A243260.

%K nonn,base

%O 1,1

%A _Anthony Sand_, Jun 02 2014