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

1,2

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

Formula

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

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 *)

Prog

(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];

Crossrefs

Cf. A008578, A151800, A175851.

Sequence in context: A160541 A378192 A286001 * A022446 A122196 A023117

Adjacent sequences: A304103 A304104 A304105 * A304107 A304108 A304109

Keyword

nonn

Author

Antti Karttunen, Jun 09 2018

Status

approved