A164338 Conway's creeper sequence

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

Offset

1,1

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).

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

Prog

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

Crossrefs

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

Cf. A114611, A114612.

Sequence in context: A288272 A247831 A161592 * A178478 A077302 A070189

Adjacent sequences: A164335 A164336 A164337 * A164339 A164340 A164341

Keyword

base,easy,nonn

Author

David W. Wilson, Aug 13 2009

Status

approved