|
%I #14 Jul 24 2022 10:44:08
%S 1,5,2,15,3,11,5,45,4,125,7,33,11,245,6,135,13,77,17,375,10,605,19,99,
%T 9,845,8,735,23,17,29,405,14,1445,15,231,31,1805,22,1125,37,1331,41,
%U 1815,12,2645,43,297,25,275,26,2535,47,539,21,2205,34,4205,53,51,59,4805,20,1215,33,1859,61,4335,38,3125,67,693
%N The Collatz or 3x+1 map (A006370) conjugated by unary-binary-encoding (A156552).
%C Collatz-conjecture can be formulated via this sequence by postulating that all iterations of a(n), starting from any n > 1, will eventually reach the cycle [2, 5, 3].
%H Antti Karttunen, <a href="/A341515/b341515.txt">Table of n, a(n) for n = 1..10000</a>
%H <a href="/index/3#3x1">Index entries for sequences related to 3x+1 (or Collatz) problem</a>
%H <a href="/index/Pri#prime_indices">Index entries for sequences computed from indices in prime factorization</a>
%F If n is odd, then a(n) = A064989(n), otherwise a(n) = A329603(n) = A341510(n,2*n).
%F a(n) = A005940(1+A006370(A156552(n))).
%o (PARI)
%o A005940(n) = { my(p=2, t=1); n--; until(!n\=2, if((n%2), (t*=p), p=nextprime(p+1))); (t); };
%o A064989(n) = {my(f); f = factor(n); if((n>1 && f[1,1]==2), f[1,2] = 0); for (i=1, #f~, f[i,1] = precprime(f[i,1]-1)); factorback(f)};
%o A156552(n) = { my(f = factor(n), p2 = 1, res = 0); for(i = 1, #f~, p = 1 << (primepi(f[i, 1]) - 1); res += (p * p2 * (2^(f[i, 2]) - 1)); p2 <<= f[i, 2]); res };
%o A329603(n) = A005940(2+(3*A156552(n)));
%o A341515(n) = if(n%2, A064989(n), A329603(n));
%Y Cf. A005940, A006370, A064989, A156552, A329603, A341510, A347115 (Möbius transform),
%Y Sequences related to iterations of this sequence: A352890, A352891, A352892, A352893, A352894, A352896, A352897, A352898, A352899.
%Y Cf. A341516 (a variant).
%K nonn
%O 1,2
%A _Antti Karttunen_, Feb 14 2021
|
