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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 (list; graph; refs; listen; history; text; internal format)
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

Rémy Sigrist, Table of n, a(n) for n = 0..10000

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

See A327539 for similar sequences.

Cf. A014263.

Sequence in context: A325263 A005992 A085050 * A067045 A083467 A061807

Adjacent sequences:  A329246 A329247 A329248 * A329250 A329251 A329252

KEYWORD

nonn,base

AUTHOR

Rémy Sigrist, Nov 30 2019

STATUS

approved

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Last modified September 20 06:59 EDT 2021. Contains 347577 sequences. (Running on oeis4.)