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 A257743 Let n'= odd part of n. If n' is 1 or prime, then a(n)=1; otherwise a(n) is 1+ the number of times the map x -> (3*x+1)' must be applied to n' in order to reach 1 or a prime. 2
 1, 1, 1, 1, 1, 1, 1, 1, 2, 1, 1, 1, 1, 1, 2, 1, 1, 2, 1, 1, 2, 1, 1, 1, 2, 1, 2, 1, 1, 2, 1, 1, 3, 1, 2, 2, 1, 1, 2, 1, 1, 2, 1, 1, 2, 1, 1, 1, 2, 2, 3, 1, 1, 2, 2, 1, 2, 1, 1, 2, 1, 1, 8, 1, 3, 3, 1, 1, 2, 2, 1, 2, 1, 1, 2, 1, 2, 2, 1, 1, 2, 1, 1, 2, 2, 1, 2 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,9 COMMENTS Conjecture: for every N>0 there exists n=n(N) such that a(n)>N. LINKS Peter J. C. Moses, Table of n, a(n) for n = 1..2000 EXAMPLE Let n=9. We have 9'=9; since (3*9+1)'=7, then a(9)=1+1=2. MATHEMATICA oddPart:=#/2^IntegerExponent[#, 2]&; a257743=Map[Length[NestWhileList[oddPart[3#+1]&, oddPart[#], !(PrimeQ[#]||#==1)&]]&, Range[200]] (*Peter J. C. Moses, May 07 2015*) PROG (PARI) step(n)=n>>=valuation(n, 2); if(isprime(n), 1, n) a(n)=my(k=1); while((n=step(n))>1, n=3*n+1; k++); k \\ Charles R Greathouse IV, May 15 2015 CROSSREFS Cf. A000040, A000265. Sequence in context: A300820 A356936 A257990 * A033272 A324907 A331295 Adjacent sequences: A257740 A257741 A257742 * A257744 A257745 A257746 KEYWORD nonn AUTHOR Vladimir Shevelev, May 07 2015 EXTENSIONS More terms from Peter J. C. Moses, May 07 2015 STATUS approved

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Last modified December 5 04:21 EST 2023. Contains 367568 sequences. (Running on oeis4.)