login
This site is supported by donations to The OEIS Foundation.

 

Logo


Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A202211 a(1)=2, a(2)=3, for n>=3, a(n)=2*(gpd(a(n-1))+gpd(a(n-2)))+1, where gpd(n) is the greatest prime divisor of n. 2
2, 3, 11, 29, 81, 65, 33, 49, 37, 89, 253, 225, 57, 49, 53, 121, 129, 109, 305, 341, 185, 137, 349, 973, 977, 2233, 2013, 181, 485, 557, 1309, 1149, 801, 945, 193, 401, 1189, 885, 201, 253, 181, 409, 1181, 3181, 8725, 7061, 1313, 817, 289 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

COMMENTS

The question about the boundedness of the sequence is equivalent to the question about its eventually periodicity. For example, the sequence defined by the same recurrence relation and initial values b(1)=2 and b(2)=5 is 2, 5, 15, 21, 25, 25, 21, 25, 25... so is periodic for n>=4 with the period {21,25,25}.

Problem.  a) do exist initials a(1) and a(2) depending on a given N for which the sequence has the least period of length>=N? b) do exist initials a(1) and a(2) for which the sequence has not any period?

Conjecture. Problem a) is answered in affirmative, while Problem b)  is answered in negative.

This sequence is eventually periodic and therefore bounded: a(61)=a(85)=85 [sic] and a(62)=a(86)=73.  [D. S. McNeil, Dec 14 2011]

LINKS

Table of n, a(n) for n=1..49.

MATHEMATICA

a[1] := 2; a[2] := 3; a[n_] := a[n] = 2(FactorInteger[a[n - 1]][[-1, 1]] + FactorInteger[a[n - 2]][[-1, 1]]) + 1; Table[a[n], {n, 50}] (* Alonso del Arte, Dec 14 2011 *)

nxt[{a_, b_}]:={b, 2(FactorInteger[a][[-1, 1]]+FactorInteger[b] [[-1, 1]])+ 1}; Transpose[NestList[nxt, {2, 3}, 120]][[1]] (* Harvey P. Dale, Dec 15 2011 *)

CROSSREFS

Cf. A006530

Sequence in context: A181956 A237038 A243896 * A104081 A267902 A003455

Adjacent sequences:  A202208 A202209 A202210 * A202212 A202213 A202214

KEYWORD

nonn

AUTHOR

Vladimir Shevelev, Dec 14 2011

STATUS

approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recent | More pages
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy .

Last modified March 26 22:28 EDT 2017. Contains 284138 sequences.