A331301 Lexicographically earliest infinite sequence such that a(i) = a(j) => f(i) = f(j), where f(n) = min(n, A225546(n)) for all other n, except for odd primes p, f(p) = 0.

1, 2, 3, 4, 3, 5, 3, 5, 6, 7, 3, 8, 3, 9, 10, 11, 3, 12, 3, 13, 14, 15, 3, 16, 17, 18, 19, 20, 3, 21, 3, 7, 22, 23, 24, 19, 3, 25, 26, 27, 3, 28, 3, 29, 30, 31, 3, 13, 32, 33, 34, 35, 3, 36, 37, 38, 39, 40, 3, 41, 3, 42, 43, 10, 44, 45, 3, 46, 47, 48, 3, 36, 3, 49, 50, 51, 52, 53, 3, 54, 17, 55, 3, 56, 57, 58, 59, 60, 3, 61, 62, 63, 64, 65, 66, 27, 3, 67, 68, 69, 3, 70, 3, 71, 72

Offset: 1

Author

Antti Karttunen, Jan 21 2020

Keywords

• nonn

Comments

For all i, j:

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

a(i) = a(j) => A064179(i) = A064179(j),

a(i) = a(j) => A064547(i) = A064547(j),

a(i) = a(j) => A302777(i) = A302777(j),

a(i) = a(j) => A331308(i) = A331308(j),

a(i) = a(j) => A331287(i) = A331287(j),

a(i) = a(j) => A331592(i) = A331592(j).

Links

• Antti Karttunen, Table of n, a(n) for n = 1..100000

Crossrefs

Cf. A019565, A225546, A305801, A331174, A331288.

Cf. also A064179, A064547, A302777, A331308, A331287, A331592.

Programs

PARI

up_to = 10000;
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; };
Aux331301(n) = if((n%2)&&isprime(n),0,A331288(n)); \\ Needs also code from A331288.
v331301 = rgs_transform(vector(up_to, n, Aux331301(n)));
A331301(n) = v331301[n];