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

Author

N. J. A. Sloane, Nov 27 2007

Keywords

• nonn
• easy

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

Crossrefs

Cf. A133422, A133419.

Programs

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 *)

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

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)

Extensions

More terms from Sean A. Irvine, Mar 29 2010

Comment clarified by Chai Wah Wu, Mar 04 2018