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

1,2

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

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))).

Prog

(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.

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.

Sequence in context: A077198 A046110 A296091 * A126889 A205030 A278250

Adjacent sequences: A352889 A352890 A352891 * A352893 A352894 A352895

Keyword

nonn

Author

Antti Karttunen, Apr 08 2022

Status

approved