

A329249


Starting from n: as long as the decimal representation starts with an odd number, multiply the largest such prefix by 2; a(n) corresponds to the final value.


2



0, 2, 2, 6, 4, 20, 6, 24, 8, 28, 20, 22, 22, 26, 24, 60, 26, 64, 28, 68, 20, 42, 22, 46, 24, 200, 26, 204, 28, 208, 60, 62, 62, 66, 64, 240, 66, 244, 68, 248, 40, 82, 42, 86, 44, 280, 46, 284, 48, 288, 200, 202, 202, 206, 204, 220, 206, 224, 208, 228, 60, 222
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OFFSET

0,2


COMMENTS

As long as we have a number whose decimal representation is the concatenation of odd number, say u, and a possibly empty string of even digits allowing leading zeros, say v, we replace this number with the concatenation of u*2 and v; eventually only even digits remain.


LINKS



FORMULA

a(n) >= n with equality iff n belongs to A014263.
a(2*n+1) = a(4*n+2).
a(10*k + v) = 10*a(k) + v for any k >= 0 and v in {0, 2, 4, 6, 8}.
a(5^k) = 2*10^k for any k >= 0 (the ratio a(n)/n is unbounded).


EXAMPLE

For n = 127:
 127 gives 127*2 = 254,
 254 gives 25*2 followed by 4 = 504,
 504 gives 5*2 followed by 04 = 1004,
 1004 gives 1*2 followed by 004 = 2004,
 2004 has only even digits, so a(127) = 2004.


MATHEMATICA

{0}~Join~Array[FixedPoint[If[AllTrue[#, EvenQ], FromDigits@ #, FromDigits@ Flatten@ Join[2 IntegerDigits@ FromDigits[First[#]], Last[#]] &@ TakeDrop[#, Position[#, _?OddQ][[1, 1]] ] ] &@ IntegerDigits[#] &, #] &, 61] (* Michael De Vlieger, Dec 01 2019 *)


PROG

(PARI) a(n) = if (n==0, 0, n%2, a(2*n), 10*a(n\10)+(n%10))


CROSSREFS



KEYWORD

nonn,base


AUTHOR



STATUS

approved



