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
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
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