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

Author

Alessandro Polcini, Oct 03 2018

Keywords

• nonn

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.

Examples

			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.
		

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

Crossrefs

Cf. A087272, A270570.

Programs

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;
}

Mathematica

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

PARI

a(n) = {while (!isprime(n), if (n % 2, n = 3*n+1, n = n/2);); n;} \\ Michel Marcus, Oct 28 2018

Formula

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