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 A127789 Record indices of 2^h(n)/(3^t(n)*n), where h and t are the number of halving resp. tripling steps in the '3x + 1' problem. 6
 1, 3, 7, 9, 505, 559, 745, 993 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,2 COMMENTS Original name: In the '3x + 1' problem we would expect a positive integer n to be approximately equal to 2^j / 3^k where j is the number of halving steps and k is the number of '3x + 1' steps required to reach 1. The numbers in this sequence are those for which 2^j / (n*3^k) sets a new record. Eric Roosendaal calls 2^j / (n*3^k) the residue of n and conjectures that 993 yields the highest residue. - T. D. Noe, Apr 08 2007 It has been verified that the next value, if it exists, is larger than 2^32 ~ 4.3e9. We do not need an "escape clause" (as for A006577, A006666, A006667, ...) in this sequence since the unlikely case of a possibly undefined ratio is irrelevant for the list of records. - M. F. Hasler, May 07 2018 LINKS Eric Roosendaal, On the 3x+1 Problem PROG (PARI) (c(n, c=[0, 0])=while(n>1, bittest(n, 0)&&c++&&(n=n*3+1)&&next; n\=2; c++); c); m=1; for(n=1, oo, m<<(t=c(n))>n*3^t||next; m=n*3^t/2^t; print1(n", ")) \\ M. F. Hasler, May 07 2018 CROSSREFS Cf. A006370 (Collatz map), A014682 (condensed version using (3n+1)/2). Cf. A006666 (halving steps), A006667 (tripling steps), A006577 (total). Sequence in context: A152607 A118559 A189244 * A112105 A065501 A144385 Adjacent sequences:  A127786 A127787 A127788 * A127790 A127791 A127792 KEYWORD more,nonn AUTHOR Paul Boddington, Apr 04 2007 EXTENSIONS New name from M. F. Hasler, May 07 2018 STATUS approved

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Last modified April 9 09:59 EDT 2020. Contains 333348 sequences. (Running on oeis4.)