A120214 Start with 1013 and repeatedly reverse the digits and add 2 to get the next term.

1013, 3103, 3015, 5105, 5017, 7107, 7019, 9109, 9021, 1211, 1123, 3213, 3125, 5215, 5127, 7217, 7129, 9219, 9131, 1321, 1233, 3323, 3235, 5325, 5237, 7327, 7239, 9329, 9241, 1431, 1343, 3433, 3345, 5435, 5347, 7437, 7349, 9439, 9351, 1541, 1453, 3543

Offset: 1

Author

Klaus Brockhaus, Jun 11 2006

Keywords

• nonn
• base

Comments

Let T(S,Q) be the sequence obtained by starting with S and repeatedly reversing the digits and adding Q to get the next term. This is T(1013,2). 1013 is the first S for which T(S,2) reaches a cycle of length 90. The cycle is simply the first 90 terms, which then repeat. A full period is given in the table.

Links

• Klaus Brockhaus, Table of n, a(n) for n = 1,...,90
• N. J. A. Sloane and others, Sequences of RADD type, OEIS wiki.
• Index entries for linear recurrences with constant coefficients, signature (0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1).

Crossrefs

Cf. A117521, A118514, A120215, A120216, A120217, A120218.

Programs

Mathematica

NestList[IntegerReverse[#]+2&,1013,50] (* Requires Mathematica version 10 or later *) (* Harvey P. Dale, Aug 16 2016 *)