A133421 Image of n under one application of the "7x+1" map.

8, 1, 1, 2, 1, 3, 50, 4, 3, 5, 78, 6, 92, 7, 5, 8, 120, 9, 134, 10, 7, 11, 162, 12, 5, 13, 9, 14, 204, 15, 218, 16, 11, 17, 7, 18, 260, 19, 13, 20, 288, 21, 302, 22, 15, 23, 330, 24, 344, 25, 17, 26, 372, 27, 11, 28, 19, 29, 414, 30, 428, 31, 21, 32, 13, 33, 470, 34, 23, 35, 498

Offset

1,1

Comments

The 7x+1 map sends x to x/2 if x is even, x/3 if x is odd and divisible by 3, x/5 if x is not divisible by 6 and divisible by 5, otherwise 7x+1.

Links

Harvey P. Dale, Table of n, a(n) for n = 1..10000

Tomás Oliveira e Silva, The px+1 problem

Index entries for sequences related to 3x+1 (or Collatz) problem

Formula

From Chai Wah Wu, Mar 04 2018: (Start)

a(n) = 2*a(n-30) - a(n-60) for n > 60.

G.f.: x*(6*x^58 + x^57 + x^56 + 2*x^55 + x^54 + 3*x^53 + 48*x^52 + 4*x^51 + 3*x^50 + 5*x^49 + 76*x^48 + 6*x^47 + 90*x^46 + 7*x^45 + 5*x^44 + 8*x^43 + 118*x^42 + 9*x^41 + 132*x^40 + 10*x^39 + 7*x^38 + 11*x^37 + 160*x^36 + 12*x^35 + 5*x^34 + 13*x^33 + 9*x^32 + 14*x^31 + 202*x^30 + 15*x^29 + 204*x^28 + 14*x^27 + 9*x^26 + 13*x^25 + 5*x^24 + 12*x^23 + 162*x^22 + 11*x^21 + 7*x^20 + 10*x^19 + 134*x^18 + 9*x^17 + 120*x^16 + 8*x^15 + 5*x^14 + 7*x^13 + 92*x^12 + 6*x^11 + 78*x^10 + 5*x^9 + 3*x^8 + 4*x^7 + 50*x^6 + 3*x^5 + x^4 + 2*x^3 + x^2 + x + 8)/(x^60 - 2*x^30 + 1). (End)

Mathematica

Table[Nest[Which[EvenQ[#], #/2, Divisible[#, 3], #/3, Divisible[#, 5], #/5, True, 7#+1]&, n, 1], {n, 75}] (* Harvey P. Dale, Nov 05 2011 *)

Prog

(PARI) a(n)=if(n%2, if(n%3, if(n%5, 7*n+1, n/5), n/3), n/2) \\ Charles R Greathouse IV, Sep 02 2015
(Python)
from __future__ import division
def A133421(n):
    return n//2 if not n % 2 else (n//3 if not n % 3 else (n//5 if not n % 5 else 7*n+1)) # Chai Wah Wu, Mar 04 2018

Crossrefs

Cf. A133422, A133419.

Sequence in context: A010153 A360970 A363918 * A128881 A154015 A300727

Adjacent sequences: A133418 A133419 A133420 * A133422 A133423 A133424

Keyword

nonn,easy

Author

N. J. A. Sloane, Nov 27 2007

Extensions

More terms from Sean A. Irvine, Mar 29 2010

Comment clarified by Chai Wah Wu, Mar 04 2018

Status

approved