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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.) 6
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 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

COMMENTS

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

LINKS

Table of n, a(n) for n=1..54.

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 * A340685 A203026 A189539

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

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Last modified July 24 01:14 EDT 2021. Contains 346265 sequences. (Running on oeis4.)