cp's OEIS Frontend

A352892 Next even term in the trajectory of map x -> A341515(x), when starting from x=n; a(1) = 1. Here A341515 is the Collatz or 3x+1 map (A006370) conjugated by unary-binary-encoding (A156552).

%I A352892 #19 Apr 09 2022 13:24:16
%S A352892 1,2,2,6,2,2,2,12,4,8,2,14,2,18,6,24,2,6,2,54,10,50,2,28,4,98,8,150,2,
%T A352892 2,2,48,14,242,6,70,2,338,22,108,2,8,2,294,12,578,2,56,4,20,26,726,2,
%U A352892 12,10,300,34,722,2,26,2,1058,20,96,14,18,2,1014,38,32,2,140,2,1682,18,1734,6,50,2,216,16,1922,2,686
%N A352892 Next even term in the trajectory of map x -> A341515(x), when starting from x=n; a(1) = 1. Here A341515 is the Collatz or 3x+1 map (A006370) conjugated by unary-binary-encoding (A156552).
%H A352892 Antti Karttunen, <a href="/A352892/b352892.txt">Table of n, a(n) for n = 1..10000</a>
%H A352892 Antti Karttunen, <a href="/A352892/a352892.txt">Data supplement: n, a(n) computed for n = 1..65537</a>
%H A352892 <a href="/index/3#3x1">Index entries for sequences related to 3x+1 (or Collatz) problem</a>
%H A352892 <a href="/index/Pri#prime_indices">Index entries for sequences computed from indices in prime factorization</a>
%F A352892 a(n) = A348717(A341515(n)).
%F A352892 For all n >= 1, a(2n) = A353268(2n), a(2n-1) = A348717(2n-1).
%F A352892 a(p) = 2 for all primes p.
%F A352892 For n > 1, a(n) = A005940(1+A139391(A156552(n))).
%o A352892 (PARI)
%o A352892 A005940(n) = { my(p=2, t=1); n--; until(!n\=2, if((n%2), (t*=p), p=nextprime(p+1))); (t); };
%o A352892 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 A352892 A156552(n) = { my(f = factor(n), p, 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 A352892 A329603(n) = A005940(2+(3*A156552(n)));
%o A352892 A341515(n) = if(n%2, A064989(n), A329603(n));
%o A352892 A348717(n) = { my(f=factor(n)); if(#f~>0, my(pi1=primepi(f[1, 1])); for(k=1, #f~, f[k, 1] = prime(primepi(f[k, 1])-pi1+1))); factorback(f); }; \\ From A348717
%o A352892 A352892(n) = A348717(A341515(n));
%o A352892 (PARI) A352892(n) = if(1==n, n, n = A341515(n); while(n%2, n = A341515(n)); (n)); \\ A slower alternative.
%Y A352892 Cf. A000040, A005940, A064989, A156552, A329603, A341515, A348717.
%Y A352892 Cf. also A139391, A352893, A352894, A352896, A352897, A352898, A352899, A353267.
%Y A352892 Coincides with A353268 on even n, and with A348717 on odd n.
%K A352892 nonn
%O A352892 1,2
%A A352892 _Antti Karttunen_, Apr 08 2022