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

1,1

Links

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

Example

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

Mathematica

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

Prog

(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, ", ")))

Crossrefs

Cf. A000079, A006370, A006577, A196871.

Sequence in context: A274167 A145265 A244161 * A258935 A275929 A240794

Adjacent sequences: A362956 A362957 A362958 * A362960 A362961 A362962

Keyword

nonn

Author

Hugo Pfoertner, May 18 2023

Status

approved