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A120688 Let f(0)=m; f(n+1)= c + d lpf(f(n)), where lpf(n) is the largest prime factor of n (A006530). For any m, for sufficiently large n the sequence f(n) oscillates. In A120684,A120685 the values d=c=1 were considered. Here we consider d=1, c=2 and this allows us to divide integers in 4 classes: C4 (m such that f(n)=4, which is a fixed point); C5 (m such that f(n)=5, then oscillates between 5,7,9); C7 (m such that f(n)=7, then oscillates between 7,9,5); C9 (m such that f(n)=9, then oscillates between 9,5,7); In A120686 we present C5 as the one that includes 5. In A120687 we present C7 as the one that includes 7. In A120688 (here) we present C9 as the one that includes 9. 3
3, 6, 9, 12, 13, 17, 18, 23, 24, 26, 27, 29, 34, 36, 39, 43, 46, 48, 51, 52, 54, 58, 59, 65, 68, 69, 72, 73, 78, 81, 85, 86, 87, 91, 92, 96, 101, 102, 104, 107, 108, 115, 116, 117, 118, 119, 129, 130, 131, 136, 138, 139, 143, 144, 145, 146, 153, 156, 157, 161, 162 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,1

COMMENTS

Note that if f(n) is not prime then f(n+1)= 2 + lpf(f(n)) <= 2 + f(n)/2 and the sequence decreases. If f(n) is prime and 2+f(n) is prime, the sequence will decrease when 2k+f(n) is not prime, which must occur for k>2. The bottom limit case is the cycle (5 7 9). The only other possibility occurs for 2^k numbers that go to the fixed point 4 because 2+lpf(2^k)=2+2=4.

LINKS

Table of n, a(n) for n=0..60.

EXAMPLE

Oscillation between 5,7,9:

2+lpf(5)=2+5=7; 2+lpf(7)=2+7=9; 2+lpf(9)=2+3=5.

Fixed point is 4: 2+lpf(4)=2+2=4.

MATHEMATICA

fi = Function[n, FactorInteger[n][[ -1, 1]] + 2]; mn = Map[(NestList[fi, #, 6][[ -1]]) &, Range[2, 200]]; Cc4 = Flatten[Position[mn, 4]] + 1; Cc5 = Flatten[Position[mn, 5]] + 1; Cc7 = Flatten[Position[mn, 7]] + 1; Cc9 = Flatten[Position[mn, 9]] + 1; Cc9

CROSSREFS

Cf. A120687, A120686, A120684, A072268, A006530.

Sequence in context: A257220 A092452 A230215 * A102014 A168045 A288522

Adjacent sequences:  A120685 A120686 A120687 * A120689 A120690 A120691

KEYWORD

nonn

AUTHOR

Carlos Alves, Jun 25 2006

STATUS

approved

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Last modified November 12 09:01 EST 2019. Contains 329052 sequences. (Running on oeis4.)