A362959 Numbers k such that the Collatz orbit that begins with k does not contain an odd prime afterwards.

4, 5, 8, 16, 21, 32, 42, 64, 84, 85, 113, 128, 168, 170, 227, 256, 336, 340, 341, 453, 512, 672, 680, 682, 906, 909, 1024, 1344, 1360, 1364, 1365, 1812, 1813, 1818, 2048, 2417, 2688, 2720, 2728, 2730, 3624, 3626, 3636, 3637, 4096, 5376, 5440, 5456, 5460, 5461, 7248

Offset: 1

Author

Hugo Pfoertner, May 18 2023

Keywords

• nonn

Examples

			a(11) = 113, because its Collatz orbit 340, 170, 85, 256, 128, 64, 32, 16, 8, 4, 2 avoids odd primes.
		

Links

• Hugo Pfoertner, Table of n, a(n) for n = 1..10010

Crossrefs

Cf. A000079, A006370, A006577, A196871.

Programs

Mathematica

Select[Range[4, 7500], NoneTrue[Rest@ NestWhileList[If[EvenQ[#], #/2, 3 # + 1] &, #, # > 1 &], And[OddQ[#], PrimeQ[#]] &] &] (* Michael De Vlieger, May 18 2023 *)

PARI

cm(k) = {while (k>1, k=if(k%2,3*k+1,k/2); if(isprime(k),break)); k};
for (k=3, 7500, if(cm(k)==2, print1(k,", ")))