A323831 a(0) = 5; thereafter a(n) is obtained by doubling a(n-1) and repeatedly deleting any string of identical digits.

5, 10, 20, 40, 80, 160, 320, 640, 1280, 2560, 5120, 10240, 20480, 40960, 81920, 163840, 327680, 6360, 12720, 250, 5, 10, 20, 40, 80, 160, 320, 640, 1280, 2560, 5120, 10240, 20480, 40960, 81920, 163840, 327680, 6360, 12720, 250

Offset

0,1

Comments

Periodic with period length 20.

Conjecture: If we start with any nonnegative number, and repeatedly double it and apply the "repeatedly delete any run of identical digits" operation described here, we eventually reach one of 0, 1, or 5.

In other words, the conjecture is that eventually we reach 0 or join the trajectory shown here or the trajectory shown in A323830.

The number of steps to reach 0, 1, or 5 is given in A323832.

Links

Paolo Xausa, Table of n, a(n) for n = 0..1000

Index entries for linear recurrences with constant coefficients, signature (0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1).

Formula

a(n+1) = A321801(2*a(n)). For general numbers, the "repeatedly delete any run of identical digits" operation corresponds to repeatedly applying A321801. - Chai Wah Wu, Feb 11 2019

Mathematica

dad[n_]:=FromDigits[FixedPoint[Flatten[Select[Split[#], Length[#]==1&]]&, IntegerDigits[2n]]]; NestList[dad, 5, 100] (* Paolo Xausa, Nov 14 2023 *)

Crossrefs

Cf. A000079, A320487, A321801, A321802, A323830, A323832.

Sequence in context: A107486 A210677 A193839 * A020714 A146523 A102260

Adjacent sequences: A323828 A323829 A323830 * A323832 A323833 A323834

Keyword

nonn,base,easy

Author

N. J. A. Sloane, Feb 03 2019

Status

approved