A327539 Starting from n: as long as the decimal representation starts with a positive even number, divide the largest such prefix by 2; a(n) corresponds to the final value.

0, 1, 1, 3, 1, 5, 3, 7, 1, 9, 5, 11, 3, 13, 7, 15, 1, 17, 9, 19, 5, 11, 11, 13, 3, 15, 13, 17, 7, 19, 15, 31, 1, 33, 17, 35, 9, 37, 19, 39, 5, 11, 11, 13, 11, 15, 13, 17, 3, 19, 15, 51, 13, 53, 17, 55, 7, 57, 19, 59, 15, 31, 31, 33, 1, 35, 33, 37, 17, 39, 35, 71

Offset: 0

Author

Rémy Sigrist, Nov 29 2019

Keywords

• nonn
• base
• easy

Comments

For n > 0, as long as we have a number whose decimal representation is the concatenation of a positive even number, say u, and a possibly empty string of odd digits, say v, we replace this number with the concatenation of u/2 and v; eventually only odd digits remain.

Examples

			For n = 10000:
- 10000 gives 10000/2 = 5000,
- 5000 gives 5000/2 = 2500,
- 2500 gives 2500/2 = 1250,
- 1250 gives 125/2 = 625,
- 625 gives 62/2 followed by 5 = 315,
- 315 has only odd digits, so a(10000) = 315.
		

Links

• Rémy Sigrist, Table of n, a(n) for n = 0..10000
• Rémy Sigrist, Logarithmic scatterplot of the first 1000000 terms
• Rémy Sigrist, Scatterplot of the ordinal transform of the first 1000000 terms

Crossrefs

See A329249, A329424 and A329428 for similar sequences.

Cf. A007283, A014261, A020714, A005009, A005010, A215145.

Programs

Mathematica

Array[FixedPoint[If[AllTrue[#, OddQ], FromDigits@ #, FromDigits@ Flatten@ Join[IntegerDigitsFromDigits[First[#]]/2, Last[#]] &@ TakeDrop[#, Position[#, ?EvenQ][[-1, -1]] ] ] &@ IntegerDigits[#] &, #] &, 71] (* _Michael De Vlieger, Dec 01 2019 *)

PARI

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

Formula

a(n) <= n with equality iff n = 0 or n belongs to A014261.

a(2*n) = a(n).

a(10*k + v) = 10*a(k) + v for any k >= 0 and v in {1, 3, 5, 7, 9}.

a(n) = 1 iff n is a power of 2.

a(n) = 3 iff n belongs to A007283.

a(n) = 5 iff n belongs to A020714.

a(n) = 7 iff n belongs to A005009.

a(n) = 9 iff n belongs to A005010.

a(n) = a(n+1) iff n belongs to A215145.