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 A335552 Triangle T(n,k) read by rows: in the Josephus problem with n initial numbers on a line: eliminate each second and reverse left-right-direction of elimination. T(n,k) is the (n-k+1)st element removed, 1<=k<=n. 1
 1, 3, 1, 3, 1, 4, 1, 5, 3, 4, 1, 5, 3, 6, 4, 3, 7, 1, 5, 6, 4, 3, 7, 1, 5, 8, 6, 4, 9, 1, 5, 3, 7, 8, 6, 4, 9, 1, 5, 3, 7, 10, 8, 6, 4, 11, 3, 7, 1, 5, 9, 10, 8, 6, 4, 11, 3, 7, 1, 5, 9, 12, 10, 8, 6, 4, 9, 1, 13, 5, 3, 7, 11, 12, 10, 8, 6, 4, 9, 1, 13, 5, 3, 7, 11, 14, 12, 10, 8, 6, 4, 11, 3, 15 (list; table; graph; refs; listen; history; text; internal format)
 OFFSET 1,2 LINKS Georg Fischer, Table of n, a(n) for n = 1..1000 K. Matsumoto, T. Nakamigawa, M. Watanabe, On the switchback vertion of Josephus Problem, Yokohama Math. J. 53 (2007) 83, function f_k(n). EXAMPLE The triangle starts 1 3 1 3 1 4 1 5 3 4 1 5 3 6 4 3 7 1 5 6 4 3 7 1 5 8 6 4 9 1 5 3 7 8 6 4 9 1 5 3 7 10 8 6 4 11 3 7 1 5 9 10 8 6 4 11 3 7 1 5 9 12 10 8 6 4 9 1 13 5 3 7 11 12 10 8 6 4 9 1 13 5 3 7 11 14 12 10 8 6 4 11 3 15 7 1 5 9 13 14 12 10 8 6 4 11 3 15 7 1 5 9 13 16 14 12 10 8 6 4 1 17 9 13 5 3 7 11 15 16 14 12 10 8 6 4 1 17 9 13 5 3 7 11 15 18 16 14 12 10 8 6 4 3 19 11 15 7 1 5 9 13 17 18 16 14 12 10 8 6 4 3 19 11 15 7 1 5 9 13 17 20 18 16 14 12 10 8 6 4 MAPLE sigr := proc(n, r) floor(n/2^r) ; end proc: # A063695 f := proc(n) local ndigs, fn, k ; ndigs := convert(n, base, 2) ; fn := 0 ; for k from 2 to nops(ndigs) by 2 do fn := fn+op(k, ndigs)*2^(k-1) end do; fn ; end proc: g := proc(t, n) local r; if t =1 then 0 ; elif t > 1 then r := ilog2( (n-1)/(t-1) ) ; (-2)^r*(f( sigr(2*n-1, r) )+f( sigr(n-1, r) )-2*t+3) ; end if; end proc: ft := proc(t, n) f(n-1)+1+g(t, n) ; end proc: for n from 1 to 20 do for t from 1 to n-1 do printf("%3d ", ft(t, n)) ; end do: printf("\n") ; end do: CROSSREFS Cf. A090569 (column k=1). Sequence in context: A201662 A274473 A280526 * A306841 A095660 A290080 Adjacent sequences: A335549 A335550 A335551 * A335553 A335554 A335555 KEYWORD nonn,tabl AUTHOR R. J. Mathar, Jun 22 2020 STATUS approved

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Last modified March 22 22:02 EDT 2023. Contains 361434 sequences. (Running on oeis4.)