A078441 - OEIS

%I #30 Feb 17 2023 08:32:31

%S 1,12,28,98,98,386,943,1494,1680,2987,2987,2987,2987,2987,7083,7083,

%T 7083,57346,57346,57346,57346,57346,57346,57346,57346,252548,252548,

%U 331778,331778,524289,596310,596310,596310,596310,596310,596310,596310,596310,596310,596310,2886352,3247146,3247146,3247146,3247146,3247146,3247146,3264428,3264428,3264428,3264428,3264428,4585418,4585418

%N a(n) begins the first chain of n consecutive positive integers that have equal h-values, where h(k) is the length of the finite sequence k, f(k), f(f(k)), ...., 1 in the Collatz (or 3x + 1) problem. (The earliest "1" is meant.)

%C Recall that f(n) = n/2 if n is even; = 3n + 1 if n is odd.

%H Karl-Heinz Hofmann, <a href="/A078441/b078441.txt">Table of n, a(n) for n = 1..255</a>

%e 28, 29, 30 is the first chain of three consecutive positive integers n, n+1, n+2 such that h(n) = h(n+1) = h(n+2). Hence a(3)=28.

%t t = Differences@ Table[Length@ NestWhileList[If[EvenQ@ #, #/2, 3 # + 1] &, n, # != 1 &], {n, 10^5}]; {1}~Join~Table[SequencePosition[t, ConstantArray[0, n - 1]][[1, 1]], {n, 2, 25}] (* _Michael De Vlieger_, Sep 14 2016, Version 10.1 *)

%Y Cf. A008908 (Values of h(k)), A153330 (Differences in adjacent h(k)).

%K nonn

%O 1,2

%A _Joseph L. Pe_, Dec 31 2002

%E More terms from _Michel ten Voorde_ Jun 20 2003

%E a(18)-a(21) corrected and a(22)-a(54) from _Donovan Johnson_, Nov 14 2010

%E a(1)=1 prepended by _Dmitry Kamenetsky_, Sep 14 2016