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 A319936 Numbers n with more than one Collatz tripling steps whose odd Collatz trajectory does not contain primes. 0
 113, 227, 453, 906, 909, 1812, 1813, 1818, 2417, 3624, 3626, 3636, 3637, 7248, 7252, 7253, 7272, 7281, 9669, 14496, 14504, 14544, 14549, 14562, 14563, 19338, 28992, 29008, 29013, 29088, 29124, 29125, 30559, 38676, 38677, 38833, 38835, 45839, 54327, 57984 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,1 COMMENTS The starting number n itself is not counted in the trajectory, otherwise prime numbers like 113 or 227 wouldn't appear in this sequence. The "odd Collatz trajectory" of a number n is the subset of odd numbers of the full Collatz trajectory of n. LINKS EXAMPLE 113 is in this sequence because 113*3+1 = 340; 340/2 = 170; 170/2 = 85; 85*3+1 = 256, which goes to 1. The trajectory has 2 (> 1) tripling steps and 85 isn't a prime. 114 is not in this sequence because 114/2 = 57; 57*3+1 = 172; 172/2 = 86; 86/2 = 43, which is a prime, and this trajectory has more than 1 tripling step. MATHEMATICA Select[Range[3, 60000], And[Count[#, _?OddQ] > 1, NoneTrue[Rest@ #, PrimeQ]] &@ NestWhileList[If[EvenQ@ #, #/2, 3 # + 1] &, #, # > 2 &, 1, Infinity, -1] &] (* Michael De Vlieger, Nov 07 2018 *) PROG (JAVA) for(int i = 0; i < DIM; i++) {     if(!collatzAtLeastOnePrime(c) && collatzTriplingSteps(c) > 1)         System.out.print(c + ", "); } boolean collatzAtLeastOnePrime(int i) {     //first step outside the while loop...   if(i % 2 == 0)         i /= 2;     else         i = 3 * i + 1;   //...otherwise prime numbers like 113 or 227 would be excluded     while(i > 1) {         if(i % 2 == 0) {             i /= 2;         }         else {             if(BigInteger.valueOf(i).isProbablePrime(10))                 return true;             i = 3 * i + 1;         }     }     return false; } CROSSREFS Cf. A002450, A006577. Sequence in context: A142426 A309617 A210512 * A142700 A142002 A142917 Adjacent sequences:  A319933 A319934 A319935 * A319937 A319938 A319939 KEYWORD nonn AUTHOR Alessandro Polcini, Oct 10 2018 STATUS approved

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Last modified September 20 16:50 EDT 2021. Contains 347586 sequences. (Running on oeis4.)