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A133419 Image of n under one application of the "5x+1" map. 10
6, 1, 1, 2, 26, 3, 36, 4, 3, 5, 56, 6, 66, 7, 5, 8, 86, 9, 96, 10, 7, 11, 116, 12, 126, 13, 9, 14, 146, 15, 156, 16, 11, 17, 176, 18, 186, 19, 13, 20, 206, 21, 216, 22, 15, 23, 236, 24, 246, 25, 17, 26, 266, 27, 276, 28, 19, 29, 296, 30, 306, 31, 21, 32, 326, 33, 336, 34, 23, 35 (list; graph; refs; listen; history; text; internal format)
OFFSET
1,1
COMMENTS
The 5x+1 map sends x to x/2 if x is even, x/3 if x is odd and divisible by 3, otherwise 5x+1.
LINKS
Tomás Oliveira e Silva, The px+1 problem
FORMULA
From Chai Wah Wu, Mar 04 2018: (Start)
a(n) = 2*a(n-6) - a(n-12) for n > 12.
G.f.: x*(4*x^10 + x^9 + x^8 + 2*x^7 + 24*x^6 + 3*x^5 + 26*x^4 + 2*x^3 + x^2 + x + 6)/(x^12 - 2*x^6 + 1). (End)
MATHEMATICA
Table[If[EvenQ[n], n/2, If[Mod[n, 3] == 0, n/3, 5*n + 1]], {n, 1, 80}] (* Stefan Steinerberger, Feb 16 2008 *)
Table[Which[EvenQ[n], n/2, Divisible[n, 3], n/3, True, 5n+1], {n, 70}] (* Harvey P. Dale, Jul 08 2018 *)
PROG
(PARI) a(n)=if(n%2, if(n%3, 5*n+1, n/3), n/2) \\ Charles R Greathouse IV, Sep 02 2015
CROSSREFS
Cf. A133420.
Sequence in context: A364129 A336179 A350034 * A010134 A019713 A155824
KEYWORD
nonn,easy
AUTHOR
N. J. A. Sloane, Nov 27 2007
EXTENSIONS
More terms from Stefan Steinerberger, Feb 16 2008
Comment clarified by Chai Wah Wu, Mar 04 2018
STATUS
approved

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Last modified March 2 04:55 EST 2024. Contains 370460 sequences. (Running on oeis4.)