A235224 a(0) = 0, and for n > 0, a(n) = largest k such that A002110(k-1) <= n, where A002110(k) gives the k-th primorial number.

0, 1, 2, 2, 2, 2, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4

Offset

0,3

Comments

For n > 0: a(n) = (length of row n in A235168) = A055642(A049345(n)).

For n > 0, a(n) gives the length of primorial base expansion of n. Also, after zero, each value n occurs A061720(n-1) times. - Antti Karttunen, Oct 19 2019

Links

Reinhard Zumkeller, Table of n, a(n) for n = 0..10000

Index entries for sequences related to primorial base

Formula

From Antti Karttunen, Oct 19 2019: (Start)

a(n) = A061395(A276086(n)).

For all n >= 0, a(n) >= A267263(n).

For all n >= 1, A000040(a(n)) > A328114(n). (End)

Maple

A235224 := proc(n)
    local k;
    if n = 0 then
        0;
    else
        for k from 0 do
            if A002110(k-1) > n then
                return k-1 ;
            end if;
        end do:
    end if;
end proc: # R. J. Mathar, Apr 19 2021

Mathematica

primorial[n_] := Times @@ Prime[Range[n]];
a[n_] := TakeWhile[primorial /@ Range[0, n], # <= n &] // Length;
Table[a[n], {n, 0, 100}] (* Jean-François Alcover, Oct 27 2021 *)

Prog

(Haskell)
a235224 n = length $ takeWhile (<= n) a002110_list
(PARI) A235224(n) = { my(s=0, p=2); while(n, s++; n = n\p; p = nextprime(1+p)); (s); }; \\ Antti Karttunen, Oct 19 2019
(PARI) A235224(n, p=2) = if(!n, n, if(n<p, 1, 1+A235224(n\p, nextprime(p+1)))); \\ (Recursive implementation) - Antti Karttunen, Oct 19 2019

Crossrefs

Cf. A000040, A002110, A049345, A055642, A061395, A061720, A084558, A267263, A276086, A235168, A328114, A328404, A328405, A328406.

Sequence in context: A321857 A186313 A165020 * A069624 A092139 A084558

Adjacent sequences: A235221 A235222 A235223 * A235225 A235226 A235227

Keyword

nonn

Author

Reinhard Zumkeller, Jan 05 2014

Extensions

Name corrected to match the data by Antti Karttunen, Oct 19 2019

Status

approved