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A372450 a(n) = k, if A086893(k) is the first term of A086893 reached on the trajectory of reduced Collatz-function R, when starting from 2n-1, or -1 if no term of A086893 is ever encountered. 1
1, 2, 3, 4, 4, 4, 4, 6, 4, 4, 5, 6, 4, 6, 4, 6, 4, 6, 4, 4, 6, 4, 4, 6, 4, 4, 6, 6, 4, 4, 6, 6, 4, 4, 4, 6, 6, 7, 4, 4, 6, 6, 7, 4, 4, 6, 6, 6, 6, 4, 4, 6, 4, 6, 6, 6, 7, 4, 4, 4, 6, 4, 6, 4, 6, 4, 4, 4, 6, 4, 6, 6, 6, 6, 4, 9, 4, 6, 4, 6, 6, 6, 6, 6, 4, 6, 4, 6, 4, 4, 4, 6, 4, 4, 6, 4, 6, 6, 4, 6, 9, 4, 4, 6, 4, 4, 8, 6 (list; graph; refs; listen; history; text; internal format)
OFFSET
1,2
COMMENTS
The length of the binary expansion of the first term of A086893 that comes along when starting from x = 2*n-1 and then repeating the operation x -> A000265(3*x+1). If 2n-1 itself is in A086893, then its binary length is used.
Terms A016789(n) = 2, 5, 8, 11, 14, 17, ... occur only once in this sequence because A086893(A016789(n)) are all multiples of 3: 3, 21, 213, 1365, 13653, 87381, 873813, 5592405, 55924053, 357913941, ..., while the terms of A075677 never are. Note that all terms > 1 of A086893 are just one or two invocations of R away from 1.
LINKS
EXAMPLE
a(11) = 5 because the first term of A086893 that occurs on the trajectory of 21 (= 2*11-1) is 21 = A086893(5).
a(14) = 6 because the first term of A086893 that occurs on the trajectory of 27 (= 2*14-1) is A372443(39) = 53 = A086893(6).
PROG
(PARI)
A000265(n) = (n>>valuation(n, 2));
A000523(n) = logint(n, 2);
A086893(n) = (if(n%2, 2^(n+1), 2^(n+1)+2^(n-1))\3);
A372358(n) = bitxor(n, A086893(1+A000523(n)));
A372450(n) = { n=2*n-1; while(A372358(n)>0, n=A000265(3*n+1)); (1+A000523(n)); };
CROSSREFS
Sequence in context: A029106 A064004 A195849 * A087827 A136528 A263252
KEYWORD
nonn
AUTHOR
Antti Karttunen, May 03 2024
STATUS
approved

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Last modified June 16 02:19 EDT 2024. Contains 373416 sequences. (Running on oeis4.)