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).

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, 2, 2, 48, 14, 242, 6, 70, 2, 338, 22, 108, 2, 8, 2, 294, 12, 578, 2, 56, 4, 20, 26, 726, 2, 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

Offset: 1

Author

Antti Karttunen, Apr 08 2022

Keywords

• nonn

Links

• Antti Karttunen, Table of n, a(n) for n = 1..10000
• Antti Karttunen, Data supplement: n, a(n) computed for n = 1..65537
• Index entries for sequences related to 3x+1 (or Collatz) problem
• Index entries for sequences computed from indices in prime factorization

Crossrefs

Cf. A000040, A005940, A064989, A156552, A329603, A341515, A348717.

Cf. also A139391, A352893, A352894, A352896, A352897, A352898, A352899, A353267.

Coincides with A353268 on even n, and with A348717 on odd n.

Programs

PARI

A005940(n) = { my(p=2, t=1); n--; until(!n\=2, if((n%2), (t*=p), p=nextprime(p+1))); (t); };
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)};
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 };
A329603(n) = A005940(2+(3*A156552(n)));
A341515(n) = if(n%2, A064989(n), A329603(n));
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
A352892(n) = A348717(A341515(n));

PARI

A352892(n) = if(1==n, n, n = A341515(n); while(n%2, n = A341515(n)); (n)); \\ A slower alternative.

Formula

a(n) = A348717(A341515(n)).

For all n >= 1, a(2n) = A353268(2n), a(2n-1) = A348717(2n-1).

a(p) = 2 for all primes p.

For n > 1, a(n) = A005940(1+A139391(A156552(n))).