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A120684
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Let f(0)=m; f(n+1)=1+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 between 3 and 4. Given a sufficently large n, this allows us to divide integers in two classes: C3 (m such that f(n)=3) and C4 (m such that f(n)=4). Note that then for n+1 the ones that belong to C3 will belong to C4 and vice-versa. Anyhow the two classes are independent of n. We present here C3 as the one that includes 3. In A120685 we present C4 as the one that includes 4.
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4
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3, 6, 7, 9, 12, 14, 18, 19, 21, 24, 27, 28, 29, 31, 35, 36, 38, 42, 43, 48, 49, 54, 56, 57, 58, 59, 62, 63, 67, 70, 72, 73, 76, 79, 81, 84, 86, 87, 89, 93, 95, 96, 98, 101, 103, 105, 108, 109, 112, 114, 116, 118, 124, 126, 127, 129, 131, 133, 134, 137, 140, 144, 145, 146
(list; graph; refs; listen; history; internal format)
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OFFSET
| 0,1
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EXAMPLE
| Oscillation between 3 and 4: 1+lpf(3)=1+3=4; 1+lpf(4)=1+2=3;
Other value, e.g. 7: 1+lpf(7)=1+7=8; 1+lpf(8)=1+2=3 (7 belongs to C3)
Other value, e.g. 20: 1+lpf(10)=1+5=6; 1+lpf(6)=1+3=4 (20 belongs to C4).
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MATHEMATICA
| f = Function[n, FactorInteger[n][[ -1, 1]] + 1]; mn = Map[(NestList[f, #, 8][[ -1]]) &, Range[2, 500]]; out = Flatten[Position[mn, 3]] + 1
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CROSSREFS
| Cf. A072268, A006530.
Sequence in context: A131392 A131397 A176409 * A026227 A026232 A061641
Adjacent sequences: A120681 A120682 A120683 * A120685 A120686 A120687
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KEYWORD
| nonn
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AUTHOR
| Carlos Alves (cjsalves(AT)gmail.com), Jun 25 2006
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