A243260 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.

81, 90, 99, 171, 180, 189, 261, 270, 279, 351, 360, 369, 441, 450, 459, 531, 540, 549, 621, 630, 639, 711, 720, 729, 801, 810, 819, 1071, 1080, 1089, 1161, 1170, 1179, 1251, 1260, 1269, 1341, 1350, 1359, 1431, 1440, 1449, 1521, 1530, 1539, 1611, 1620, 1629

Offset: 1

Author

Anthony Sand, Jun 02 2014

Keywords

• nonn
• base

Comments

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)).

Examples

			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.
90 + 9 = 99. 99 - 18 = 81. 81 + 9 = 90.
99 - 18 = 81. 81 + 9 = 90. 90 + 9 = 99.
171 + 9 = 180. 180 + 9 = 189. 189 - 18 = 171.
180 + 9 = 189. 189 - 18 = 171. 171 + 9 = 180.
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.
		

Links

• Anthony Sand, Table of n, a(n) for n = 1..1000

Crossrefs

Cf. A243259, A004207.

Formula

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