This site is supported by donations to The OEIS Foundation.

 Hints (Greetings from The On-Line Encyclopedia of Integer Sequences!)
 A304584 A linear mapping a(n) = x + d*n of pairs of nonnegative integers (x,d), where the pairs are enumerated by antidiagonals. 5
 0, 1, 2, 2, 5, 10, 3, 9, 17, 27, 4, 14, 26, 40, 56, 5, 20, 37, 56, 77, 100, 6, 27, 50, 75, 102, 131, 162, 7, 35, 65, 97, 131, 167, 205, 245, 8, 44, 82, 122, 164, 208, 254, 302, 352, 9, 54, 101, 150, 201, 254, 309, 366, 425, 486, 10, 65, 122, 181, 242, 305, 370, 437, 506, 577, 650, 11 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,3 COMMENTS The sequence solves the following riddle, which has been communicated by Klaus Nagel: A flea starts to jump on the nonnegative integers at time = 0 at an unknown location x >= 0 making jumps of unknown, but constant distance d >= 0 at every subsequent time step. By which strategy can the flea be captured with 100% certainty in a finite number of trials? The solution is to hit a(n) at time = n. This works for all enumerations of pairs (x,d) of integers, because eventually any combination of starting location x and jump width d will be addressed. LINKS Rainer Rosenthal, Table of n, a(n) for n = 0..10000 EXAMPLE d:   5 |  20   4 |  14  19   3 |   9  13  18   2 |   5   8  12  17   1 |   2   4   7  11  16   0 |   0   1   3   6  10  15     |________________________   x:    0   1   2   3   4   5 . a(13) = 1 + 13*3 = 40 because the 13th position in the enumeration corresponds to x=1 and d=3. MAPLE pos2pair:=proc(n) local w, k, e; w:=floor(sqrt(2*n)); if w*(w+1)>2*n then k:=w-1; else k:=w; fi; e:=n-k*(k+1)/2; return [k-e, e]; end:WhereFlea:=proc(n) local x, d, pair; pair:=pos2pair(n); x:=pair[1]; d:=pair[2]; return x+d*n; end: seq(WhereFlea(n), n=0..66); # Rainer Rosenthal, May 23 2018 CROSSREFS Cf. A304585, A304586, A304587, A305260. Sequence in context: A003228 A184713 A110182 * A193899 A208567 A273968 Adjacent sequences:  A304581 A304582 A304583 * A304585 A304586 A304587 KEYWORD nonn AUTHOR Hugo Pfoertner, May 15 2018 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 August 23 22:45 EDT 2019. Contains 326254 sequences. (Running on oeis4.)