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A090691
5x - 1 sequence starting at 50 (a(n+1) = a(n)/2 if a(n) is even, or 5*a(n)-1 if a(n) is odd).
1
50, 25, 124, 62, 31, 154, 77, 384, 192, 96, 48, 24, 12, 6, 3, 14, 7, 34, 17, 84, 42, 21, 104, 52, 26, 13, 64, 32, 16, 8, 4, 2, 1, 4, 2, 1, 4, 2, 1, 4, 2, 1, 4, 2, 1, 4, 2, 1, 4, 2, 1, 4, 2, 1, 4, 2, 1, 4, 2, 1, 4, 2, 1, 4, 2, 1, 4, 2, 1, 4, 2, 1, 4, 2, 1, 4, 2, 1, 4, 2, 1, 4, 2, 1, 4, 2, 1, 4, 2, 1
OFFSET
1,1
COMMENTS
There is a general conjecture (see, e.g., the paper of Heppner, Eine Bemerkung zum Hasse-Syracuse-Algorithmus, Arch. Math. (Basel) 31 (1978/79), 317-320, that for the 5x-1 problem there are divergent sequences (since 5 > 2^{2/(2-1)}, although for the Collatz problem 3 < 2^{2/(2-1)}). - Jean-Paul Allouche, Sep 14 2024
FORMULA
a(1) = 50, a(n+1) = a(n)/2 if a(n) even, otherwise 5*a(n) - 1.
MATHEMATICA
NestList[If[EvenQ[#], #/2, 5# - 1] &, 50, 100] (* Alonso del Arte, Aug 12 2016 *)
PROG
(Magma) [n eq 1 select 50 else IsOdd(Self(n-1)) select 5*Self(n-1)-1 else Self(n-1) div 2: n in [1..80]]; // Vincenzo Librandi, Aug 21 2016
CROSSREFS
Sequence in context: A072460 A248128 A033370 * A033980 A342903 A207149
KEYWORD
nonn,easy
AUTHOR
Daniil Khanin (daniil(AT)ispms.tsc.ru), Feb 06 2004
EXTENSIONS
More terms from Ray Chandler, Feb 08 2004
New definition by Alonso del Arte, Aug 12 2016
Definition clarified by N. J. A. Sloane, Sep 14 2024
STATUS
approved