A332900 Lexicographically earliest infinite sequence such that a(i) = a(j) => f(i) = f(j), where f(n) = 0 if n > 1 and n is a square or twice square, with f(n) = n for all other numbers.

1, 2, 3, 2, 4, 5, 6, 2, 2, 7, 8, 9, 10, 11, 12, 2, 13, 2, 14, 15, 16, 17, 18, 19, 2, 20, 21, 22, 23, 24, 25, 2, 26, 27, 28, 2, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 2, 2, 41, 42, 43, 44, 45, 46, 47, 48, 49, 50, 51, 52, 53, 2, 54, 55, 56, 57, 58, 59, 60, 2, 61, 62, 63, 64, 65, 66, 67, 68, 2, 69, 70, 71, 72, 73, 74, 75, 76, 77, 78, 79, 80, 81, 82, 83, 84, 2, 85, 2

Offset: 1

Author

Antti Karttunen, Mar 05 2020

Keywords

• nonn

Comments

For all i, j:

A324400(i) = A324400(j) => a(i) = a(j),

a(i) = a(j) => A292383(i) = A292383(j) => A292583(i) = A292583(j),

a(i) = a(j) => A332896(i) = A332896(j) => A332901(i) = A332901(j).

Links

• Antti Karttunen, Table of n, a(n) for n = 1..65537

Crossrefs

Cf. A292383, A292583, A324400, A332896, A332901.

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; };
A332900aux(n) = if((n>1)&&(issquare(n)||issquare(2*n)),0,n);
v332900 = rgs_transform(vector(up_to,n,A332900aux(n)));
A332900(n) = v332900[n];