A117817 Let T_n be the infinite sequence formed by starting with 1 and repeatedly reversing the digits and adding n to get the next term. If T_n eventually reaches a cycle, sequence gives length of that cycle, otherwise -1.

9, 81, 3, 54, 207, 30, 63, 27, 1, -1, 9, 15, 18, 72, -1, 90, 54, 13, 18, -1, 15, 9, 9, 36, 45, 18, 9, 36, 18, -1, 9, 9, 3, 36, 72, 2, 27, 18, 3, -1, 18, 57, 63, 9, 22, 90, 18, 30, 54, -1, 6, 99, 54, 13, 36, 207, 12, 63, 45, -1, 36, 27, 30, 108, 36, 264, 99, 36, 3, -1, 18, 22, 45, 90, 12, 45, 117, 192, 18, -1, 36, 45, 63, 168, 1008, 36, 24, 306, 9, -1, 99, 639, 36, 54, 144, 18, 225, 468, 1, -1, 18, 300, 189, 171, 765, 90, 45, 462, 90, -1, 9, 513, 63, 69

Offset: 1

Author

N. J. A. Sloane, following discussions with Luc Stevens, May 04 2006

Keywords

• sign
• base

Comments

a(multiple of 10) = -1 (see A117816). a(15) = -1 (see A118532). a(n) is a multiple of 9/gcd(9,n) unless it is -1. - Martin Fuller, May 12 2006

For a discussion of the -1 entries see A117816.

Links

• N. J. A. Sloane and others, Sequences of RADD type, OEIS wiki.

Crossrefs

See A117817 for the -1 entries and cross-references to T_1 through T_16.

Programs

Mathematica

ReverseNum[n_] := FromDigits[Reverse[IntegerDigits[n]]]; maxLen=10000; Table[z=1; lst={1}; While[z=ReverseNum[z]+n; !MemberQ[lst,z] && Length[lst]
				

Extensions

a(21)-a(33) from Luc Stevens, May 08 2006

a(33) onwards from T. D. Noe and Martin Fuller, May 10 2006