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

Author

Rémy Sigrist, Nov 30 2019

Keywords

• nonn
• base

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.

Examples

			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.
		

Links

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

Crossrefs

See A327539 for similar sequences.

Cf. A014263.

Programs

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 *)

PARI

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

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).