A320028 a(n) is the first prime encountered when running the Collatz algorithm (halving and tripling steps) on the number n.

2, 3, 2, 5, 3, 7, 2, 7, 5, 11, 3, 13, 7, 23, 2, 17, 7, 19, 5, 2, 11, 23, 3, 19, 13, 41, 7, 29, 23, 31, 2, 19, 17, 53, 7, 37, 19, 59, 5, 41, 2, 43, 11, 17, 23, 47, 3, 37, 19, 29, 13, 53, 41, 83, 7, 43, 29, 59, 23, 61, 31, 137, 2, 37, 19, 67, 17, 13, 53, 71, 7, 73, 37, 113, 19, 29, 59, 79, 5, 61, 41, 83, 2, 2, 43, 131

Offset

2,1

Comments

A modified version of the halving and tripling Collatz algorithm, which stops as soon as the starting number becomes a prime (instead of stopping when the starting number reaches 1).

The plot of this sequence "completes" or "fills" the lower (empty) part of plot of A270570 and evolves in a similar fashion.

Links

Alessandro Polcini, Table of n, a(n) for n = 2..10000 (a(2024) corrected by Michel Marcus, Jun 14 2022)

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

Formula

a(n) <= A087272(n). - Rémy Sigrist, Oct 08 2018

Example

a(4) is 2 because 4/2 = 2 and 2 is prime.
a(6) is 3 because 6/2 = 3 and 3 is prime.
a(15) is 23 because 15*3 + 1 = 46; 46/2 = 23 and 23 is prime.
a(18) is 7 because 18/2 = 9; 9*3 + 1 = 28; 28/2 = 14; 14/2 = 7 and 7 is prime.

Mathematica

Array[NestWhile[If[EvenQ@ #, #/2, 3 # + 1] &, #, ! PrimeQ@ # &] &, 86, 2] (* Michael De Vlieger, Nov 07 2018 *)

Prog

(Java) int collatzPrime(int i) {
    while(!BigInteger.valueOf(i).isProbablePrime(10) && i > 1) {
        if(i % 2 == 0)
            i /= 2;
        else
            i = 3 * i + 1;
    }
    return i;
}
(PARI) a(n) = {while (!isprime(n), if (n % 2, n = 3*n+1, n = n/2); ); n; } \\ Michel Marcus, Oct 28 2018

Crossrefs

Cf. A087272, A270570.

Sequence in context: A347619 A164858 A192330 * A327076 A215041 A347241

Adjacent sequences: A320025 A320026 A320027 * A320029 A320030 A320031

Keyword

nonn

Author

Alessandro Polcini, Oct 03 2018

Status

approved