The OEIS Foundation is supported by donations from users of the OEIS and by a grant from the Simons Foundation. Hints (Greetings from The On-Line Encyclopedia of Integer Sequences!)
 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

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recent
The OEIS Community | Maintained by The OEIS Foundation Inc.

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