A076138 - OEIS

A076138

a(1)=1; a(n+1) is the smallest integer > a(n) such that C_2k(a(n+1))=C_2k(a(n)) for k large enough, where C_m(n) is the modified Collatz map iterated m times on n ( x->x/2 if x is even x->(3x+1)/2 if x is odd).

%I #5 Mar 30 2012 18:39:09

%S 1,4,5,6,11,14,15,19,20,21,24,25,26,27,33,34,35,43,44,45,46,47,56,57,

%T 58,59,60,61,62,63,64,72,74,76,77,78,79,80,81,82,83,84,85,96,98,99,

%U 100,101,102,103,104,105,106,107,108,109,110,113,130,131,132,133,134,135

%N a(1)=1; a(n+1) is the smallest integer > a(n) such that C_2k(a(n+1))=C_2k(a(n)) for k large enough, where C_m(n) is the modified Collatz map iterated m times on n ( x->x/2 if x is even x->(3x+1)/2 if x is odd).

%F a(n+1) = min (k>a(n) : A076057(k)=A076057(a(n))). a(n) seems to be asymptotic to 2*n and a(n)=2*n for some n (5, 14, 43, 54, 72, 93, ...)

%Y Cf. A006513, A076057.

%K nonn

%O 1,2

%A _Benoit Cloitre_, Oct 31 2002