

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.


6



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
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OFFSET

0,4


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.


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


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.


EXAMPLE

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.


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 *)


PROG

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


CROSSREFS

See A329249, A329424 and A329428 for similar sequences.
Cf. A007283, A014261, A020714, A005009, A005010, A215145.
Sequence in context: A336650 A327656 A098985 * A072963 A161955 A276234
Adjacent sequences: A327536 A327537 A327538 * A327540 A327541 A327542


KEYWORD

nonn,base,easy


AUTHOR

Rémy Sigrist, Nov 29 2019


STATUS

approved



