

A323830


a(0) = 1; thereafter a(n) is obtained by doubling a(n1) and repeatedly deleting any string of identical digits.


5



1, 2, 4, 8, 16, 32, 64, 128, 256, 512, 1024, 2048, 4096, 8192, 16384, 32768, 636, 1272, 25, 50, 1, 2, 4, 8, 16, 32, 64, 128, 256, 512, 1024, 2048, 4096, 8192, 16384, 32768, 636, 1272, 25, 50, 1, 2, 4, 8, 16, 32, 64, 128, 256, 512, 1024, 2048, 4096, 8192, 16384, 32768, 636, 1272, 25, 50
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OFFSET

0,2


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 A323831.
The number of steps to reach 0, 1, or 5 is given in A323832.


LINKS

Colin Barker, 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

From Colin Barker, Feb 03 2019: (Start)
G.f.: (1 + 2*x)*(1 + 4*x^2 + 16*x^4 + 64*x^6 + 256*x^8 + 1024*x^10 + 4096*x^12 + 16384*x^14 + 636*x^16 + 25*x^18) / (1  x^20).
a(n) = a(n20) for n>19.
(End)
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


EXAMPLE

After a(15) = 32768 we get 65536 which becomes 636 after deleting "55". Then doubling 636 we get 1272, then 2544 which becomes 25 after deleting "44", then 50, then 100 which becomes 1 after deleting "00", and now the sequence repeats.


PROG

(PARI) Vec((1 + 2*x)*(1 + 4*x^2 + 16*x^4 + 64*x^6 + 256*x^8 + 1024*x^10 + 4096*x^12 + 16384*x^14 + 636*x^16 + 25*x^18) / (1  x^20) + O(x^40)) \\ Colin Barker, Feb 03 2019


CROSSREFS

Cf. A000079, A320487, A321801, A321802, A323831, A323832.
See A035615 for a classic related base2 sequence.
Sequence in context: A220051 A220493 A320487 * A118655 A249169 A247208
Adjacent sequences: A323827 A323828 A323829 * A323831 A323832 A323833


KEYWORD

nonn,base,easy


AUTHOR

N. J. A. Sloane, Feb 03 2019, following a suggestion from Yukun Yao.


STATUS

approved



