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A346139
Numbers k that require fewer than k steps to reach 1 under the 3x+1 map.
0
1, 2, 4, 8, 10, 12, 13, 16, 17, 20, 21, 22, 23, 24, 25, 26, 28, 29, 30, 32, 33, 34, 35, 36, 37, 38, 39, 40, 42, 43, 44, 45, 46, 48, 49, 50, 51, 52, 53, 56, 57, 58, 59, 60, 61, 64, 65, 66, 67, 68, 69, 70, 72, 74, 75, 76, 77, 78, 79, 80, 81, 84, 85, 86, 87, 88
OFFSET
1,2
COMMENTS
Numbers k such that A006577(k) < k.
Is 5 the only positive number neither in this sequence, nor in A228014 (cf. Caldwell, Honaker)?
EXAMPLE
The trajectory of 13 under repeated applications of the Collatz map starts 13, 40, 20, 10, 5, 16, 8, 4, 2, 1, requiring 9 steps to reach 1. 9 < 13, so 13 is a term of the sequence.
MATHEMATICA
nsteps[n_] := -1 + Length @ NestWhileList[If[OddQ[#], 3 # + 1, #/2] &, n, # > 1 &]; Select[Range[100], nsteps[#] < # &] (* Amiram Eldar, Jul 14 2021 *)
PROG
(PARI) a006370(n) = if(n%2==0, n/2, 3*n+1)
is(n) = my(x=n, i=0); while(1, if(x==1, if(i < n, return(1), return(0))); x=a006370(x); i++)
CROSSREFS
KEYWORD
nonn
AUTHOR
Felix Fröhlich, Jul 14 2021
STATUS
approved