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Search: id:A138751
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| 2, 7, 3, 17, 7, 29, 11, 41, 13, 17, 67, 79, 23, 89, 29, 29, 31, 127, 137, 37, 149, 163, 43, 47, 197, 53, 211, 59, 223, 59, 257, 67, 71, 281, 79, 307, 317, 331, 89, 89, 97, 367, 97, 389, 101, 401, 431, 449, 127, 461, 127, 127, 487, 127, 131, 137, 137, 547, 557, 149
(list; graph; listen)
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OFFSET
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1,1
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COMMENT
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Composing the map A138750 with A007918 to the left and
restricting it to the primes makes it a
mapping from primes into primes which is a natural generalization of
the Collatz problem to primes.
(Looking at parity would not be interesting for primes, so using "mod
3" is the simplest nontrivial generalization.)
The only even prime p=2 is the only fixed point of this map, and all
odd primes seem to end up
in the loop 7 -> 17 -> 11 -> 7, after a number of steps given in A138752.
The sequence A124123 lists the primes which do not occur in the
present sequence.
See A138750 for further information.
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LINKS
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Georges Brougnard, Definition of GB-sequences.
Index entries for sequences related to 3x+1 (or Collatz) problem
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FORMULA
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a(n)=A007918( A138750( A000040( n )))
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EXAMPLE
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a(1)=nextprime( 2/2 )=2, a(2) = nextprime( 2*3 )=7, a(3) =
nextprime( 5/2 )=7, ...
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PROGRAM
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(PARI) A138751(n) = { n=prime(n); nextprime( if( n%3==2, ceil(n/2), 2*n ))}
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CROSSREFS
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Cf. A124123, A007918, A138750, A138752-A138753.
Sequence in context: A120861 A099130 A076992 this_sequence A112303 A089124 A117809
Adjacent sequences: A138748 A138749 A138750 this_sequence A138752 A138753 A138754
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KEYWORD
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easy,nonn
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AUTHOR
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M. F. Hasler (www.univ-ag.fr/~mhasler), Mar 28 2008
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