cp's OEIS Frontend

A372446 a(n) = A372358(A372443(n)).

%I A372446 #10 May 03 2024 12:43:10
%S A372446 14,28,10,26,18,62,116,44,14,92,50,78,60,122,82,222,260,232,114,46,44,
%T A372446 78,252,106,138,410,354,774,1064,218,2,1366,336,276,228,16,8,2,22,0,0,
%U A372446 0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0
%N A372446 a(n) = A372358(A372443(n)).
%C A372446 These are the bitmasks (or symmetric differences) obtained when the n-th iterate of 27 with Reduced Collatz-function R [= A372443(n), where R(n) = A000265(3*n+1)] is xored with that term of A086893 that has the same binary length. The binary expansions of the terms of A086893 are always of the form 10101...0101 (i.e., alternating 1's and 0's starting and ending with 1) when the binary length is odd, and of the form 110101...0101 (i.e., 1 followed by alternating 1's and 0's, and ending with 1) when n is even. Note that for all n >= 1, R(A086893(2n-1)) = 1, and R(A086893(2n)) = 5 (with R(5) = 1), so the first zero here, a(39) = 0 indicates that the iteration will soon have reached the terminal 1, and indeed, A372443(41) = 1.
%H A372446 <a href="/index/3#3x1">Index entries for sequences related to 3x+1 (or Collatz) problem</a>
%o A372446 (PARI)
%o A372446 A000265(n) = (n>>valuation(n,2));
%o A372446 A000523(n) = logint(n,2);
%o A372446 A086893(n) = (if(n%2, 2^(n+1), 2^(n+1)+2^(n-1))\3);
%o A372446 A372358(n) = bitxor(A086893(1+A000523(n)),n);
%o A372446 A372443(n) = { my(x=27); while(n, x=A000265(3*x+1); n--); (x); };
%o A372446 A372446(n) = A372358(A372443(n));
%Y A372446 Column 14 of A372361.
%Y A372446 Cf. A000265, A075677, A086893, A372358, A372443.
%K A372446 nonn
%O A372446 0,1
%A A372446 _Antti Karttunen_, May 03 2024