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 A362959 Numbers k such that the Collatz orbit that begins with k does not contain an odd prime afterwards. 1
 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 (list; graph; refs; listen; history; text; internal format)
 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

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Last modified June 16 07:19 EDT 2024. Contains 373423 sequences. (Running on oeis4.)