OFFSET
1,2
COMMENTS
Starting with the natural numbers, make 2 passes removing every 2nd number, 3 passes removing every 3rd number, etc.
Is the limiting value of a(n+1)/a(n)=3?
Since 1/(1-1/n)^n converges to e (as n -> inf), a(n+1)/a(n) converges to e. - Hiroaki Yamanouchi, Nov 27 2014
LINKS
EXAMPLE
The 1st pass removes 2, 4, 6, 8, 10, etc. The 2nd pass (also with 2) removes 3, 7, 11, 15, 19, etc. Then there are 3 passes removing every 3rd number, of which the 1st pass removes 9, 21, 33, 45, ..., the 2nd removes 13, 29, 49, ..., and the 3rd removes 17, 41, 73, ...; then there are 4 passes with 4; 5 passes with 5; etc.
MATHEMATICA
A247105 = Reap[Quiet @ For[n=1, n<28, n++, m = n; For[i=n, i >= 1, i--, For[j=1, j <= i, j++, t = Floor[(m*i)/(i-1)]; While[t - Floor[t/i] >= m, t -= 1]; om = m; m = t+1]]; Sow[om]]][[2, 1]] (* Jean-François Alcover, Nov 28 2014, translated and adapted from Hiroaki Yamanouchi's Python script *)
PROG
(PARI) copydropmult(v, m)=vector(#v-#v\m, i, v[(i-1)*m\(m-1)+1])
alim(n)=my(r=vector(n, i, i), j=2, k=1); while(j<#r, r=copydropmult(r, j); if(k++>j, j++; k=1)); r
(Python)
for n in range(1, 101):
m = n
for i in range(n, 1, -1):
for j in range(i):
t = m * i // (i - 1)
while t - t // i >= m:
t -= 1
m = t + 1
print(f"{n} {m}") # Hiroaki Yamanouchi, Nov 28 2014
CROSSREFS
KEYWORD
nonn
AUTHOR
Sergio Pimentel, Nov 18 2014
EXTENSIONS
More values from Franklin T. Adams-Watters, Nov 21 2014
a(12)-a(20) from Alois P. Heinz, Nov 26 2014
a(21)-a(27) from Hiroaki Yamanouchi, Nov 27 2014
STATUS
approved