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A164338 Conway's creeper sequence 3
12334444, 55667777, 123334444, 556667777, 1233334444, 5566667777, 12333334444, 55666667777, 123333334444, 556666667777, 1233333334444, 5566666667777, 12333333334444, 55666666667777, 123333333334444 (list; graph; refs; listen; history; text; internal format)
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

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]

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

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Last modified November 14 22:17 EST 2019. Contains 329134 sequences. (Running on oeis4.)