A258822 - OEIS

A258822

Number of times that k iterations of n under the '3x+1' map yield k for some k.

0, 1, 0, 0, 0, 0, 1, 1, 0, 1, 0, 0, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 2, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 1, 1, 1, 1, 0, 1, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 1, 0, 0, 0, 0, 1, 0, 1, 0, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 1, 1, 1, 0, 0, 0, 0, 0

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OFFSET

1,24

COMMENTS

This sequence uses the definition in A006370: if n is odd, n -> 3*n+1, if n is even, n -> n/2.

The number 3 appears first at a(63105). Do all nonnegative numbers appear? See A258824.

LINKS

Paolo Xausa, Table of n, a(n) for n = 1..10000

Index entries for sequences related to 3x+1 (or Collatz) problem

EXAMPLE

For n = 6, the '3x+1' map is as follows: 6 -> 3 -> 10 -> 5 -> 16 -> 8 -> 4 -> 2 -> 1. Here the number of iterations is 8. However, after the k-th iteration, the result does not equal k. Thus a(6) = 0.

For n = 7, the '3x+1' map is as follows: 7 -> 22 -> 11 -> 34 -> 17 -> 52 -> 26 -> 13 -> 40 -> 20 -> 10 -> 5 -> 16 -> 8 -> 4 -> 2 -> 1. Only after 10 iterations do we arrive at 10. Since this is the only time this happens, a(7) = 1.

MATHEMATICA

A258822[n_]:=Count[MapIndexed[{#1}==#2-1&, NestWhileList[If[OddQ[#], 3#+1, #/2]&, n, #>1&]], True]; Array[A258822, 100] (* Paolo Xausa, Nov 06 2023 *)

PROG

(PARI) Tvect(n)=v=[n]; while(n!=1, if(n%2, k=(3*n+1); v=concat(v, k); n=k); if(!(n%2), k=n/2; v=concat(v, k); n=k)); v

for(n=1, 200, d=Tvect(n); c=0; for(i=1, #d, if(d[i]==i-1, c++)); print1(c, ", "))

CROSSREFS

Cf. A006370, A258772, A070165.

Sequence in context: A127282 A138954 A245811 * A353373 A064530 A307832

Adjacent sequences: A258819 A258820 A258821 * A258823 A258824 A258825

KEYWORD

nonn

AUTHOR

Derek Orr, Jun 11 2015

STATUS

approved