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
KEYWORD
nonn,base,easy
AUTHOR
N. J. A. Sloane, Feb 03 2019
STATUS
approved