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A276260 Odd primes p such that p is in the trajectory of p+1 under the Collatz 3x+1 map (A014682). 1
5, 13, 17, 53, 61, 107, 251, 283, 1367 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

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

Table of n, a(n) for n=1..9.

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

MATHEMATICA

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

PROG

(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"; }

}

(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

CROSSREFS

Cf. A014682, A276290.

Sequence in context: A120130 A087484 A019382 * A145040 A195549 A125146

Adjacent sequences:  A276257 A276258 A276259 * A276261 A276262 A276263

KEYWORD

nonn,more

AUTHOR

Marina Ibrishimova, Aug 26 2016

STATUS

approved

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Last modified March 29 21:48 EDT 2017. Contains 284288 sequences.