A276260 Odd primes p such that p is in the trajectory of p+1 under the Collatz 3x+1 map (A014682).

5, 13, 17, 53, 61, 107, 251, 283, 1367

Offset: 1

Author

Marina Ibrishimova, Aug 26 2016

Keywords

• nonn
• more

Comments

a(10) > 10^7 if it exists. - Felix Fröhlich, Aug 26 2016

a(10) > 10^9 if it exists. - Charles R Greathouse IV, Aug 26 2016

a(10) > 10^12 if it exists. - Charles R Greathouse IV, Sep 07 2016

Links

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

Crossrefs

Cf. A014682, A276290.

Programs

JavaScript

function isit_collatz_prime(p)
{
    var cur = p+1;
    while(cur != p && cur != 2)
    {
       if(cur%2!=0)
       {
           cur = 3*cur + 1;
       }else
       {
        cur = cur/2;
       }
    }
    if(cur === p ){return "p is a Collatz prime";}
    else {return "p is not a Collatz prime";}
}

Mathematica

Select[Prime@ Range[2, 10^5], MemberQ[NestWhileList[If[EvenQ[#], #/2, 3 # + 1] &, # + 1, # > 1 &], #] &] (* Michael De Vlieger, Aug 26 2016 *)

PARI

next_collatz_iteration(n) = if(n%2==1, return(3*n+1), return(n/2))
is(n) = if(n%2==1 && ispseudoprime(n), my(k=n+1); while(k > 1, k=next_collatz_iteration(k); if(k==n, return(1)))); 0 \\ Felix Fröhlich, Aug 26 2016

PARI

has(n)=my(k=n+1); k>>=valuation(k,2); while(k>1, k+=(k+1)>>1; k>>=valuation(k,2); if(k==n, return(1))); 0
forprime(p=3,1e9, if(has(p), print1(p", "))) \\ Charles R Greathouse IV, Aug 26 2016