This site is supported by donations to The OEIS Foundation.

 Hints (Greetings from The On-Line Encyclopedia of Integer Sequences!)
 A230107 Define a sequence by b(1)=n, b(k+1)=b(k)+(sum of digits of b(k)); a(n) is the number of steps needed to reach a term in A004207, or a(n) = -1 if the sequence never joins A004207. 4
 0, 0, -1, 0, 52, -1, 11, 0, -1, 51, 50, -1, 49, 10, -1, 0, 48, -1, 9, 50, -1, 49, 0, -1, 47, 48, -1, 0, 8, -1, 49, 46, -1, 47, 48, -1, 45, 0, -1, 7, 46, -1, 47, 6, -1, 45, 44, -1, 0, 46, -1, 5, 5, -1, 45, 44, -1, 43, 4, -1, 4, 0, -1, 4, 44, -1, 43, 3, -1, 0 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,5 COMMENTS Looking at b(k) mod 9 shows that a(n) = -1 whenever n is a multiple of 3 (since then the b sequence is disjoint from A004207). Conjecture: the b sequence, for any starting value n, will eventually merge with one of A000004 (the zero sequence), A004207, A016052 or A016096. LINKS EXAMPLE For n=3, A016052 never meets A004207, so a(3) = -1. For n=5, A007618 meets A004207 at the 53rd term, 620, so a(5) = 53. MAPLE read transforms; # to get digsum M:=2000; # f(s) returns the sequence k->k+digsum(k) starting at s f:=proc(s) global M; option remember; local n, k, s1; s1:=[s]; k:=s; for n from 1 to M do  k:=k+digsum(k); s1:=[op(s1), k]; od: end; # g(s) returns (x, p), where x = first number in common between # f(1) and f(s), and p is the position where it occurred. # If f(1), f(s) are disjoint for M terms, returns (-1, -1) S1:=convert(f(1), set): g:=proc(s) global f, S1; local t1, p, S2, S3; S2:=convert(f(s), set); S3:= S1 intersect S2; t1:=min(S3); if (t1 = infinity) then RETURN(-1, -1); else   member(t1, f(s), 'p'); RETURN(t1, p-1); fi; end; [seq(g(n)[2], n=1..20)]; PROG (Haskell) import Data.Maybe (fromMaybe) a230107 = fromMaybe (-1) . f (10^5) 1 1 1 where    f k i u j v | k <= 0    = Nothing                | u < v     = f (k - 1) (i + 1) (a062028 u) j v                | u > v     = f (k - 1) i u (j + 1) (a062028 v)                | otherwise = Just j CROSSREFS Cf. A004207, A016052, A007618, A006507, A016096, A062028, A230299. Sequence in context: A230299 A308235 A022079 * A275412 A100990 A298573 Adjacent sequences:  A230104 A230105 A230106 * A230108 A230109 A230110 KEYWORD sign,base AUTHOR N. J. A. Sloane and Reinhard Zumkeller, Oct 15 2013; corrected Oct 20 2013 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 October 16 16:18 EDT 2019. Contains 328101 sequences. (Running on oeis4.)