%I #30 Sep 14 2024 09:44:41
%S 50,25,124,62,31,154,77,384,192,96,48,24,12,6,3,14,7,34,17,84,42,21,
%T 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,
%U 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
%N 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).
%C 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
%F a(1) = 50, a(n+1) = a(n)/2 if a(n) even, otherwise 5*a(n) - 1.
%t NestList[If[EvenQ[#], #/2, 5# - 1] &, 50, 100] (* _Alonso del Arte_, Aug 12 2016 *)
%o (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
%Y Cf. A008880, A037238.
%K nonn,easy,changed
%O 1,1
%A Daniil Khanin (daniil(AT)ispms.tsc.ru), Feb 06 2004
%E More terms from _Ray Chandler_, Feb 08 2004
%E New definition by _Alonso del Arte_, Aug 12 2016
%E Definition clarified by _N. J. A. Sloane_, Sep 14 2024