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A063041
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Image of n under Collatz-2 map, a generalization of the classical '3x+1' - function: instead of dividing an even number by 2 a nonprime will be divided by its smallest prime factor and a prime will be multiplied not by 3 but by its prime-predecessor.
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5
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3, 7, 2, 16, 3, 36, 4, 3, 5, 78, 6, 144, 7, 5, 8, 222, 9, 324, 10, 7, 11, 438, 12, 5, 13, 9, 14, 668, 15, 900, 16, 11, 17, 7, 18, 1148, 19, 13, 20, 1518, 21, 1764, 22, 15, 23, 2022, 24, 7, 25, 17, 26, 2492, 27, 11, 28, 19, 29, 3128, 30, 3600, 31, 21, 32, 13, 33, 4088, 34, 23
(list; graph; refs; listen; history; internal format)
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OFFSET
| 2,1
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LINKS
| Matthew M. Conroy, Home page (listed instead of email address)
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FORMULA
| a(n) = if n prime then (n * pp(n) + 1) else (n / lpd(n)) for n > 1 where pp(n) = if n > 2 then Max{p prime | p < n} else 1; [prime-predecessor] and lpd(n) = if n > 2 then Min{p prime | p < n and p divides n} else 1; [A020639]
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EXAMPLE
| a(17) = 17 * 13 = 222 as 17 is prime and 13 is the largest prime < 17; a(4537) = 349 as 4537 = 13 * 349 hence lpd(4537) = 13; other examples in A063042, A063043, A063044.
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CROSSREFS
| Cf. A063042, A063043, A063044, A063045, A063046.
Sequence in context: A159759 A197837 A163917 * A144713 A134731 A133368
Adjacent sequences: A063038 A063039 A063040 * A063042 A063043 A063044
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KEYWORD
| nonn,easy
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AUTHOR
| Reinhard Zumkeller (reinhard.zumkeller(AT)gmail.com), Jul 07 2001
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EXTENSIONS
| More terms from Matthew M. Conroy, Jul 15 2001
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