1,2

This is a variation of A138752, counting the number of

iterations of A138754

needed to get any number for the second time, while A138752 stops

counting somehow

arbitrarily at 1=primepi(2) or 4=primepi(7).

The map A138754 is a variation of the Collatz map

where parity of the integers is replaced by p mod 3 for the primes.

For the Collatz map, we have the only fixed point 0=f(0) and

all other numbers seem to end up in the cycle 1->4->2->1.

Here the only fixed point is 1=A138754(1), and all other

numbers seem to end up in the cycle 4 -> 7 -> 5 -> 4

(corresponding to primes 7 -> 17 -> 11 -> 7).

Depending on which number among primepi({2,7,11,17})

is reached first, A138753(n) = A138752(n)+1,+3,+2 resp. +1.

(A138752(n) is the length of the so-called GB-sequence starting with prime(n).)

M. F. Hasler, Table of n, a(n), for n=1,...,500

Georges Brougnard, Definition of GB-sequences.

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

A138753(n) = min { k>0 | A138754^k(n) = A138754^m(n) for some m>=0, m<k }

If n is not in {1,4,5,7}, then A138753(n)=1+A138753(A138754(n))

a(1)=1 since after 1 step we find 1 again.

a(4)=3 since 4 -> 7 -> 5 -> 4 under A138754.

(PARI) A138753(n, c=0, t=[1, 1, 1]) = { until( t[c++%3+1]==n=A138754(n), t[c%3+1]=n); c}

Cf. A124123, A006577, A138750-A138754, A138755-A138756 (record values/indices of A138753).

Sequence in context: A004485 A057113 A060134 this_sequence A069197 A021692 A107793

Adjacent sequences: A138750 A138751 A138752 this_sequence A138754 A138755 A138756

nonn

M. F. Hasler (www.univ-ag.fr/~mhasler), Apr 01 2008