A304106 Ordinal transform of A175851.

1, 2, 3, 1, 4, 2, 5, 3, 1, 1, 6, 4, 7, 5, 2, 2, 8, 6, 9, 7, 3, 3, 10, 8, 4, 4, 1, 1, 11, 9, 12, 10, 5, 5, 2, 2, 13, 11, 6, 6, 14, 12, 15, 13, 7, 7, 16, 14, 8, 8, 3, 3, 17, 15, 9, 9, 4, 4, 18, 16, 19, 17, 10, 10, 5, 5, 20, 18, 11, 11, 21, 19, 22, 20, 12, 12, 6, 6, 23, 21, 13, 13, 24, 22, 14, 14, 7, 7, 25, 23, 15, 15, 8, 8, 1, 1, 26, 24, 16, 16

Offset: 1

Author

Antti Karttunen, Jun 09 2018

Keywords

• nonn

Comments

Ordinal transform of the ordinal transform of the nextprime function, A151800(1..) = 2, 3, 5, 5, 7, 7, 11, 11, 11, 11, ...

Links

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

Crossrefs

Cf. A008578, A151800, A175851.

Programs

Mathematica

A175851[n_] := If[!CompositeQ[n], 1, n - NextPrime[n, -1] + 1];
b[_] = 0;
a[n_] := a[n] = With[{t = A175851[n]}, b[t] = b[t] + 1];
Array[a, 105] (* Jean-François Alcover, Dec 21 2021 *)

PARI

up_to = 65537;
A151800(n) = nextprime(1+n);
ordinal_transform(invec) = { my(om = Map(), outvec = vector(length(invec)), pt); for(i=1, length(invec), if(mapisdefined(om,invec[i]), pt = mapget(om, invec[i]), pt = 0); outvec[i] = (1+pt); mapput(om,invec[i],(1+pt))); outvec; };
v304106 = ordinal_transform(ordinal_transform(vector(up_to,n,A151800(n))));
A304106(n) = v304106[n];

Formula

For all n >= 1, a(A008578(n)) = n.