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A233341 Least number m for which n applications of the mapping r(k) = k - (greatest prime divisor of k) map m to 0. 3
1, 4, 8, 12, 25, 30, 32, 48, 63, 70, 75, 80, 165, 176, 189, 192, 289, 306, 315, 320, 385, 392, 507, 520, 575, 598, 621, 644, 841, 858, 957, 968, 1015, 1044, 1071, 1088, 1105, 1122, 1425, 1444, 1463, 1470, 1771, 1782, 1935, 1978, 2145, 2156, 2303, 2350, 2397 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

COMMENTS

r(m) = 1 if and only if m = 1 or m is a prime.  Conjecture:  Every positive integer divides infinitely many terms of A233341.

LINKS

Clark Kimberling, Table of n, a(n) for n = 1..200

EXAMPLE

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.

MATHEMATICA

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}]

CROSSREFS

Cf. A233342.

Sequence in context: A278602 A059992 A050570 * A102110 A055079 A081833

Adjacent sequences:  A233338 A233339 A233340 * A233342 A233343 A233344

KEYWORD

nonn,easy

AUTHOR

Clark Kimberling, Dec 07 2013

STATUS

approved

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Last modified June 29 05:29 EDT 2017. Contains 288859 sequences.