Year-end appeal: Please make a donation to the OEIS Foundation to support ongoing development and maintenance of the OEIS. We are now in our 61st year, we have over 378,000 sequences, and we’ve reached 11,000 citations (which often say “discovered thanks to the OEIS”).
%I #27 May 05 2024 15:44:00
%S 1,4,8,12,25,30,32,48,63,70,75,80,165,176,189,192,289,306,315,320,385,
%T 392,507,520,575,598,621,644,841,858,957,968,1015,1044,1071,1088,1105,
%U 1122,1425,1444,1463,1470,1771,1782,1935,1978,2145,2156,2303,2350,2397
%N Least number m for which n applications of the mapping r(k) = k - (greatest prime divisor of k) map m to 0.
%C r(m) = 1 if and only if m = 1 or m is a prime. Conjecture: Every positive integer divides infinitely many terms of this sequence.
%C Sequence is empirically observed to be strictly increasing for n <= 1000, in contrast to similar map in A050710. - _Christian N. K. Anderson_, May 05 2023
%C Observe that for ~4/7 of the first thousand terms, r(a(n)) = a(n-1); e.g., a(12)=80, r(80)=75=a(11) -> 70=a(10) -> 63=a(9). However, the other ~3/7 take a different route to zero; e.g., a(9)=63 decreases by 7 at all 9 steps. Contrast A048133, where every term's iteration ends when r(k)=5. - _Christian N. K. Anderson_, May 05 2023
%H Christian N. K. Anderson, <a href="/A233341/b233341.txt">Table of n, a(n) for n = 1..1000</a> (first 200 terms from Clark Kimberling)
%F For 228 <= n <= 1000, a(n) ~ 0.8526*n^2.023 to within 4% (empirical observation). - _Christian N. K. Anderson_, May 05 2023
%e r(8) = 8 - 2 = 6; r(6) = 6 - 3 = 3; r(3) = 3 - 3 = 0. Thus 3 applications of r map 8 to 0, whereas 1 or 2 applications suffice for n < 8. Therefore, a(3) = 8.
%t z = 10000; h[n_] := h[n] = n - FactorInteger[n][[-1, 1]]; t[n_] := Drop[FixedPointList[h, n], -2]; Table[t[n], {n, 1, z}]; a = Table[Length[t[n]], {n, 1, z}]; f[n_] := First[Flatten[Position[a, n]]]; Table[f[n], {n, 1, 80}]
%Y Cf. A233342.
%K nonn,easy
%O 1,2
%A _Clark Kimberling_, Dec 07 2013