A164338 Conway's creeper sequence.

12334444, 55667777, 123334444, 556667777, 1233334444, 5566667777, 12333334444, 55666667777, 123333334444, 556666667777, 1233333334444, 5566666667777, 12333333334444, 55666666667777, 123333333334444

Offset: 1

Author

David W. Wilson, Aug 13 2009

Keywords

• base
• easy
• nonn

Comments

Trajectory of 12334444 under the RATS function A036839.

John Conway calls this sequence "the creeper" and conjectures that the RATS trajectory of every n >= 1 eventually enters a cycle or the creeper. David Wilson confirms this conjecture for n <= 10^10.

Continues with the obvious digital pattern.

Since a(n+2) = a(n) except for an added digit, this sequence can be described as a quasi-cycle of period 2 with smallest element 12334444. This is how it is treated in related sequences such as A161590, A161592 and A161593.

Links

• Reinhard Zumkeller, Table of n, a(n) for n = 1..100
• Eric Weisstein's World of Mathematics, RATS Sequence
• Index entries for linear recurrences with constant coefficients, signature (0,11,0,-10).

Crossrefs

Cf. A036839 (RATS function), A161590, A161592, A161593.

Cf. A114611, A114612.

Programs

Haskell

a164338 n = a164338_list !! (n-1)
a164338_list = iterate a036839 12334444
-- Reinhard Zumkeller, Mar 14 2012

Formula

a(n+2) = 10 a(n) - 9996 (n odd)

a(n+2) = 10 a(n) - 9993 (n even)

a(n+4) = 11 a(n+2) - 10 a(n)

a(n + 1) = A036839(a(n)). [Reinhard Zumkeller, Mar 14 2012]

G.f.: x*(-55677770*x^3 - 12344440*x^2 + 55667777*x + 12334444)/(10*x^4 - 11*x^2 + 1). - Chai Wah Wu, Feb 08 2020