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A372443 The n-th iterate of 27 with Reduced Collatz-function R, which gives the odd part of 3n+1.

%I A372443 #18 May 10 2024 11:16:28
%S A372443 27,41,31,47,71,107,161,121,91,137,103,155,233,175,263,395,593,445,
%T A372443 167,251,377,283,425,319,479,719,1079,1619,2429,911,1367,2051,3077,
%U A372443 577,433,325,61,23,35,53,5,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1
%N A372443 The n-th iterate of 27 with Reduced Collatz-function R, which gives the odd part of 3n+1.
%H A372443 <a href="/index/3#3x1">Index entries for sequences related to 3x+1 (or Collatz) problem</a>
%F A372443 a(0) = 27; for n > 0, a(n) = R(a(n-1)), where R(n) = (3*n+1)/2^A371093(n) = A000265(3*n+1).
%F A372443 For n > 0, a(n) = R(A372444(n-1)) = A000265(1+3*A372444(n-1)).
%o A372443 (PARI)
%o A372443 R(n) = { n = 1+3*n; n>>valuation(n, 2); };
%o A372443 A372443(n) = { my(x=27); while(n, x=R(x); n--); (x); };
%Y A372443 Cf. A000265, A075677, A371093.
%Y A372443 Column 14 of A372283, Row 13 of A256598 (but only up to the first 1).
%Y A372443 Row 1 of A372560.
%Y A372443 From term 47 to the first 1 same as A088593.
%Y A372443 Sequences derived from this one or related to:
%Y A372443   A372444,
%Y A372443   A372445 column index of a(n) in array A257852,
%Y A372443   A372362 the 2-adic valuation of 1 + 3*a(n), equal to row index of a(n) in array A257852,
%Y A372443   A372447 binary lengths minus 1,
%Y A372443   A372446 a(n) xored with the term of A086893 having the same binary length,
%Y A372443   A372453 a(n) minus the term of A086893 having the same binary length.
%K A372443 nonn
%O A372443 0,1
%A A372443 _Antti Karttunen_, May 01 2024