A222617 - OEIS

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A222617

Number of integers k < n whose Collatz (3x+1) trajectory contains n.

0, 0, 0, 1, 1, 0, 0, 4, 0, 4, 2, 0, 3, 1, 0, 11, 4, 0, 0, 9, 0, 5, 1, 0, 0, 9, 0, 2, 2, 0, 1, 1, 0, 11, 5, 0, 0, 2, 0, 25, 1, 0, 0, 6, 0, 5, 3, 0, 1, 1, 0, 23, 9, 0, 0, 3, 0, 7, 1, 0, 6, 3, 0, 2, 2, 0, 2, 1, 0, 14, 7, 0, 0, 4, 0, 7, 1, 0, 0, 19, 0, 2, 2, 0, 1

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OFFSET

1,8

COMMENTS

It is assumed that Collatz trajectory ends at 1.

REFERENCES

R. K. Guy, Unsolved Problems in Number Theory, E16.

LINKS

T. D. Noe, Table of n, a(n) for n = 1..10000

EXAMPLE

a(8)=4, since 8 appears in Collatz trajectories of n < 8; similarly a(9)=0 since 9 does not appear in Collatz trajectories n < 9.

MATHEMATICA

Collatz[n_] := NestWhileList[If[EvenQ[#], #/2, 3 # + 1] &, n, # > 1 &]; nn = 100; t = Table[Collatz[n], {n, nn}]; Table[r = 0; Do[If[MemberQ[t[[i]], k], r++], {i, k - 1}]; r, {k, nn}] (* T. D. Noe, Feb 26 2013 *)

CROSSREFS

Cf. A070165.

Sequence in context: A140574 A010636 A222302 * A204695 A175435 A160214

Adjacent sequences: A222614 A222615 A222616 * A222618 A222619 A222620

KEYWORD

nonn

AUTHOR

Jayanta Basu, Feb 26 2013

STATUS

approved