A055510 -id:A055510 - cp's OEIS frontend

A055509 Number of odd primes in sequence obtained in 3x+1 (or Collatz) problem starting at n.

0, 0, 2, 0, 1, 2, 5, 0, 5, 1, 4, 2, 2, 5, 3, 0, 3, 5, 6, 1, 0, 4, 3, 2, 6, 2, 24, 5, 5, 3, 23, 0, 6, 3, 2, 5, 6, 6, 10, 1, 24, 0, 7, 4, 3, 3, 22, 2, 6, 6, 5, 2, 2, 24, 23, 5, 7, 5, 10, 3, 4, 23, 19, 0, 6, 6, 8, 3, 2, 2, 21, 5, 24, 6, 1, 6, 5, 10, 10, 1, 4, 24, 23, 0, 0, 7, 8, 4, 9, 3, 19, 3, 2, 22, 19

Offset: 1

G. L. Honaker, Jr., Jun 30 2000

nonn

Reinhard Zumkeller, Table of n, a(n) for n = 1..10000
Eric Weisstein's World of Mathematics, Collatz Problem
Wikipedia, Collatz conjecture
Index entries for sequences related to 3x+1 (or Collatz) problem

Cf. A055510.

Cf. A006370, A010051.

a055509 n = sum $ map a010051 $ takeWhile (> 2) $ iterate a006370 n -- Reinhard Zumkeller, Oct 08 2011

g:= proc(n) option remember;
   local x;
   x:= 3*n+1;
   x:= x/2^padic:-ordp(x,2);
   if isprime(n) then procname(x)+1 else procname(x) fi
end proc:
g(1):= 0:
seq(g(n/2^padic:-ordp(n,2)),n=1..100); # Robert Israel, Dec 05 2017

Join[{0}, Table[Count[NestWhileList[If[EvenQ[#], #/2, 3 # + 1] &, n, # > 1 &], ?PrimeQ] - 1, {n, 2, 94}]] (* _Jayanta Basu, Jun 15 2013 *)

A078350(n,c=0)={while(1>=valuation(n,2), isprime(n)&&c++; n=n*3+1);c} \\ M. F. Hasler, Dec 05 2017

a(n) = A078350(n) - 1 for n > 1.
a(A196871(n)) = 0. - Reinhard Zumkeller, Oct 08 2011
From Robert Israel, Dec 05 2017: (Start)
If n is odd, a(n) = a(3*n+1) + A010051(n).
If n is even, a(n) = a(n/2). (End)

More terms from Larry Reeves (larryr(AT)acm.org), Aug 09 2001

A087272 a(n) is the largest prime number in 3x+1 trajectory initiated at n.

Original entry on oeis.org

2, 5, 2, 5, 5, 17, 2, 17, 5, 17, 5, 13, 17, 53, 2, 17, 17, 29, 5, 2, 17, 53, 5, 29, 13, 1619, 17, 29, 53, 1619, 2, 29, 17, 53, 17, 37, 29, 101, 5, 1619, 2, 43, 17, 17, 53, 1619, 5, 37, 29, 29, 13, 53, 1619, 1619, 17, 43, 29, 101, 53, 61, 1619, 1619, 2, 37, 29, 101, 17, 13, 53

Offset: 2

Labos Elemer, Sep 18 2003

nonn

Rémy Sigrist, Table of n, a(n) for n = 2..10000

Cf. A025586, A055510, A087232.

c[x_] := (1-Mod[x, 2])*(x/2)+Mod[x, 2]*(3*x+1); c[1]=1; fpl[x_] := Delete[FixedPointList[c, x], -1] ofp[x_] := Part[fpl[x], Flatten[Position[PrimeQ[fpl[x]], True]]] Table[Max[ofp[w]], {w, 1, 256}]
Table[Max[Select[NestWhileList[If[EvenQ[#],#/2,3#+1]&,n,#>1&],PrimeQ]],{n,2,70}] (* Harvey P. Dale, Feb 27 2023 *)

a(n) = my (mx=2); while (n>1, if (isprime(n), mx=max(mx,n)); n=if (n%2, 3*n+1, n/2)); mx \\ Rémy Sigrist, Oct 08 2018

Offset corrected by Rémy Sigrist, Oct 08 2018

A299963 a(n) = greatest prime factor of the terms in the Collatz sequence starting at n; a(1) = 1.

Original entry on oeis.org

1, 2, 5, 2, 5, 5, 17, 2, 17, 5, 17, 5, 13, 17, 53, 2, 17, 17, 29, 5, 7, 17, 53, 5, 29, 13, 1619, 17, 29, 53, 1619, 2, 29, 17, 53, 17, 37, 29, 101, 5, 1619, 7, 43, 17, 17, 53, 1619, 5, 37, 29, 29, 13, 53, 1619, 1619, 17, 43, 29, 101, 53, 61, 1619, 1619, 2, 37

Offset: 1

Rémy Sigrist, Feb 22 2018

nonn

The value 3 cannot appear in this sequence.
The value 1619 appears 1654 times among the first 10000 terms; this is visible as a dashed horizontal line in the corresponding scatterplot.
The most frequent values among the first 10000000 terms are:
Value     Number of occurrences among the first 10000000 terms
  -------   ---------------------------------------------------
   283763   16934
  2017817   15701
     1619   15274
    55667   14706
  2717873    9913

Rémy Sigrist, Table of n, a(n) for n = 1..10000
Rémy Sigrist, Ordinal transform of the first 10000000 terms
Index entries for sequences related to 3x+1 (or Collatz) problem

Cf. A006530, A055510, A087272, A178168.

Table[Max[FactorInteger[#][[-1,1]]&/@NestWhileList[If[EvenQ[#],#/2,3#+1]&, n,#>1&]], {n,70}] (* Harvey P. Dale, Jun 22 2020 *)

a(n) = my (g=1); while (n>1, my (f=factor(n)); g=max(g,f[#f~,1]); n=if (n%2, 3*n+1, n/2)); return (g)

a(n) = A006530(A178168(n)).
a(2*n) = a(n) for any n > 1.
a(2^k) = 2 for any k > 0.

cp's OEIS Frontend

A055509 Number of odd primes in sequence obtained in 3x+1 (or Collatz) problem starting at n.

Views

Author

Keywords

Links

Crossrefs

Programs

Haskell

Maple

Mathematica

PARI

Formula

Extensions

A087272 a(n) is the largest prime number in 3x+1 trajectory initiated at n.

Views

Author

Keywords

Links

Crossrefs

Programs

Mathematica

PARI

Extensions

A299963 a(n) = greatest prime factor of the terms in the Collatz sequence starting at n; a(1) = 1.

Views

Author

Keywords

Comments

Links

Crossrefs

Programs

Mathematica

PARI

Formula