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.

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

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: A365380 A005992 A085050 * A067045 A083467 A061807

Adjacent sequences: A329246 A329247 A329248 * A329250 A329251 A329252

Keyword

nonn,base

Author

Rémy Sigrist, Nov 30 2019

Status

approved