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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).

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

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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

LINKS

Table of n, a(n) for n=1..90.

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

Cf. A008880, A037238.

Sequence in context: A072460 A248128 A033370 * A033980 A342903 A207149

Adjacent sequences: A090688 A090689 A090690 * A090692 A090693 A090694