A072141 -id:A072141 - cp's OEIS frontend

A072139 Last term of the preperiodic part of the 'Reverse and Subtract' trajectory of n, or -1 if the trajectory is completely periodic.

-1, 1, 2, 3, 4, 5, 6, 7, 8, 9, 9, 11, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 22, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 33, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 44, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 55, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 66, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 77, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 88, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 99, 99, 101, 99

Offset: 0

Klaus Brockhaus, Jun 24 2002

'Reverse and Subtract' (cf. A072137) is defined by x -> |x - reverse(x)|. For small n the positive terms are the first palindrome in the trajectory of n, so this sequence is a weak analog of A033865, which uses 'Reverse and Add'. a(1012) = 8712 is the first non-palindrome (cf. A072140). For k in A072140, A072141 or A072142 we have a(k) = -1.

			a(0) = -1, since 0 -> |0 - 0| = 0, the preperiodic part is empty; a(12) = 9, since 12 -> |12 - 21| = 9.

Cf. A033865, A072137, A072140, A072141, A072142.

A335978 Numbers m of the form abs(k - reverse(k)) for at least one k.

Original entry on oeis.org

0, 9, 18, 27, 36, 45, 54, 63, 72, 81, 90, 99, 180, 189, 198, 270, 279, 297, 360, 369, 396, 450, 459, 495, 540, 549, 594, 630, 639, 693, 720, 729, 792, 810, 819, 891, 900, 909, 990, 999, 1089, 1179, 1188, 1269, 1278, 1359, 1368, 1449, 1458, 1539, 1548, 1629, 1638, 1719, 1728, 1800, 1809, 1818, 1890, 1908, 1980, 1989, 1998, 2079

Offset: 1

Michael Greaney, Jul 03 2020

All terms are divisible by 9.
Let f(k) = k - reverse(k). Then f(reverse(k)) = -f(k), since f(reverse(k)) = reverse(k) - reverse(reverse(k)) = reverse(k) - k = - (k - reverse(k)) = -f(k).
Iteration of the function f(k) = k - reverse(k) leads to A072140, A072141, A072142, and A072143.

Michael P. Greaney, Remarkable Reversible Numbers, +plus magazine, (September 29, 2015).

Cf. A056965, A067030, A072140, A072141, A072142, A072143.

Dividing by 9 gives A334145.

A109891 Least number that requires n steps to reach 0 by repeated application of f: x -> abs(x - reverse(x)).

Original entry on oeis.org

0, 1, 10, 16, 14, 15, 13, 1011, 1017, 1037, 1027, 1014, 1013, 1028, 100143, 100135, 100145, 100134, 100103, 100195, 100137, 100227, 100114, 100128, 100194, 100107, 100307, 100277, 100413, 100345, 100429, 100215, 100444, 100237, 100433, 100335

Offset: 0

Amarnath Murthy, Jul 13 2005

Coincides with A072138 for the first 14 and many later terms.

			f(16) = 61-16 = 45, f(45) = 54-45 = 9, f(9) = 9-9 = 0. For no k < 16 exactly three steps lead to 0, hence a(3) = 16.

Cf. A072137, A072138, A072141.

Edited, corrected and extended by Klaus Brockhaus, Jul 14 2005

cp's OEIS Frontend

A072139 Last term of the preperiodic part of the 'Reverse and Subtract' trajectory of n, or -1 if the trajectory is completely periodic.

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A335978 Numbers m of the form abs(k - reverse(k)) for at least one k.

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A109891 Least number that requires n steps to reach 0 by repeated application of f: x -> abs(x - reverse(x)).

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