

A243115


Starting values of the reduced Collatz function (A014682) where 2 to the power of the "dropping time" is greater than the starting value.


0



3, 7, 11, 15, 23, 27, 31, 39, 47, 59, 63, 71, 79, 91, 95, 103, 111, 123, 127, 155, 159, 167, 175, 191, 199, 207, 219, 223, 231, 239, 251, 255, 283, 287, 303, 319, 327, 347, 359, 367, 383, 411, 415, 423, 447, 463, 479, 487, 495, 507, 511, 539, 543, 559, 575
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OFFSET

3,1


COMMENTS

a(n) is the lowest positive starting value of the reduced Collatz function such that all starting values (>1) that are congruent to a(n) (mod 2^d) have the same dropping time (d). The dropping time here counts the (3x+1)/2 and the x/2 steps as listed in A126241. A number is included in this sequence if 2^A126241(a(n)) > a(n).
Starting values that produce new record dropping times as listed in A060412 are necessarily a subset of this sequence.
If at least one iteration is carried out before checking that the absolute iterated value has become less than or equal to the absolute starting value, then a(n) is the lowest positive starting value such that all starting values (positive, zero or negative) that are congruent to a(n) (mod 2^d) have the same dropping time (d). Defined like this, the sequence would start with 0, 1, 3, 7, 11, 15, ... for a lead index value of 0.


LINKS

Table of n, a(n) for n=3..57.


EXAMPLE

3 is in this sequence because the dropping time starting with 3 is A126241(3) = 4 and 2^4 > 3.


PROG

(PARI) for(a=3, 575, d=0; x=a; until(x<=a, if(x%2, x=(x*3+1)/2, x/=2); d++); if(2^d>a, print1(a, ", ")))


CROSSREFS

Sequence in context: A160785 A095100 A036994 * A279106 A172306 A309274
Adjacent sequences: A243112 A243113 A243114 * A243116 A243117 A243118


KEYWORD

nonn


AUTHOR

K. Spage, Aug 20 2014


STATUS

approved



