A078441 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.)

1, 12, 28, 98, 98, 386, 943, 1494, 1680, 2987, 2987, 2987, 2987, 2987, 7083, 7083, 7083, 57346, 57346, 57346, 57346, 57346, 57346, 57346, 57346, 252548, 252548, 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

Offset

1,2

Comments

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

Links

Karl-Heinz Hofmann, Table of n, a(n) for n = 1..255

Example

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.

Mathematica

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 *)

Crossrefs

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

Sequence in context: A043189 A043969 A204386 * A351104 A340685 A203026

Adjacent sequences: A078438 A078439 A078440 * A078442 A078443 A078444

Keyword

nonn

Author

Joseph L. Pe, Dec 31 2002

Extensions

More terms from Michel ten Voorde Jun 20 2003

a(18)-a(21) corrected and a(22)-a(54) from Donovan Johnson, Nov 14 2010

a(1)=1 prepended by Dmitry Kamenetsky, Sep 14 2016

Status

approved