A352899 Lexicographically earliest infinite sequence such that a(i) = a(j) => f(i) = f(j), where f(n) = A352892(n), except f(n) = -n when <= 2.

1, 2, 3, 4, 3, 3, 3, 5, 6, 7, 3, 8, 3, 9, 4, 10, 3, 4, 3, 11, 12, 13, 3, 14, 6, 15, 7, 16, 3, 3, 3, 17, 8, 18, 4, 19, 3, 20, 21, 22, 3, 7, 3, 23, 5, 24, 3, 25, 6, 26, 27, 28, 3, 5, 12, 29, 30, 31, 3, 27, 3, 32, 26, 33, 8, 9, 3, 34, 35, 36, 3, 37, 3, 38, 9, 39, 4, 13, 3, 40, 41, 42, 3, 43, 21, 44, 45, 46, 3, 8, 12

Offset: 1

Author

Antti Karttunen, Apr 08 2022

Keywords

• nonn

Comments

Restricted growth sequence transform of function f(n) = -n if n < 3, and otherwise f(n) = A352892(n).

For all i, j:

A305801(i) = A305801(j) => A352898(i) = A352898(j) => a(i) = a(j),

a(i) = a(j) => A352893(i) = A352893(j),

a(i) = a(j) => A352896(i) = A352896(j).

Links

• Antti Karttunen, Table of n, a(n) 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. A305801, A329603, A341515, A348717, A352892, A352893, A352896, A352898.

Programs

PARI

up_to = 65537;
rgs_transform(invec) = { my(om = Map(), outvec = vector(length(invec)), u=1); for(i=1, length(invec), if(mapisdefined(om,invec[i]), my(pp = mapget(om, invec[i])); outvec[i] = outvec[pp] , mapput(om,invec[i],i); outvec[i] = u; u++ )); outvec; };
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));
Aux352899(n) = if(n<=2,-n,A352892(n));
v352899 = rgs_transform(vector(up_to, n, Aux352899(n)));
A352899(n) = v352899[n];