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%I A324248 #10 Feb 22 2019 19:34:24
%S A324248 27,31,47,63,71,91,103,111,127,155,159,167,191,207,223,231,239,251,
%T A324248 255,283,287,303,319,327,347,359,367,383,411,415,423,447,463,479,487,
%U A324248 495,507,511,539,543,559,575,583,603,615,623,639,667,671,679,703,719,735,743,751,763,767
%N A324248 Odd numbers with dropping time of the reduced Collatz iteration (A122458) exceeding 5.
%C A324248 Note that the Collatz conjecture is assumed. Otherwise there may exist (very large) odd numbers for which no finite dropping time exists
%C A324248 This sequence is obtained from the residue classes modulo 256 of the entries a(1) to a(19): 27, 31, 47, 63, 71, 91, 103, 111, 127, 155, 159, 167, 191, 207, 223, 231, 239, 251, 255. See the Klee-Wagon reference where the function C is C(2*n+1) = A075677(n+1) = A000265(3*n+2), for n >= 0, and dropping time is called there stopping time (on p. 225 Exercise 4 should be Exercise 5 given on p. 229, with hints on p. 309; also in the first line after (1) 'less than 5' should be replaced by 'not exceeding 5').
%C A324248 The values of (a(j)-1)/2, for j = 1..19, are 13, 15, 23, 31, 35, 45, 51, 55, 63, 77, 79, 83, 95, 103, 111, 115, 119, 125, 127.
%C A324248 The dropping times are 5 for the seven residue classes modulo 256 of 39, 79, 95, 123, 175, 199, and 219. See Klee-Wagon, Exercise 5 (a), p. 229.
%C A324248 The dropping times for a(n) are given in A324249(n).
%D A324248 Victor Klee and Stan Wagon, Old and New Unsolved Problems in Plane Geometry and Number Theory, Mathematical Association of America (1991) pp. 191-194, 225-229, 308-309.
%F A324248 Sorted sequence of the odd numbers 2*m + 1 with least positive integer k >=  6 such that fr^[k](m) < 2*m + 1, for m >= 1, where fr is the reduced Collatz function fr(m) := A075677(m+1) = A000265(3*m+2).
%e A324248 n = 1: The trajectory under the reduced Collatz function fr for (a(1) - 1)/2  = 13 is given as an example in A122456, from which the dropping time is read off as 37 = A122456(13).
%e A324248 n = 2: The dropping time of a(2) = 31 is 35 = A122456(15). The second to last trajectory number 5 is the first number < 31.
%Y A324248 Cf. A000265, A075677, A122458, A324249.
%K A324248 nonn,easy
%O A324248 1,1
%A A324248 _Wolfdieter Lang_, Feb 21 2019

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