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

Author

Joseph L. Pe, Dec 31 2002

Keywords

• nonn

Comments

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

Examples

			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.
		

Links

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

Crossrefs

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

Programs

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 *)

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