A324381 Number of nonzero digits when the n-th highly composite number is written in primorial base: a(n) = A267263(A002182(n)).

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

Offset

1,7

Links

Antti Karttunen, Table of n, a(n) for n = 1..10000

Index entries for sequences related to primorial base

Index entries for sequences related to primorial numbers

Formula

a(n) = A267263(A002182(n)).

a(n) <= A324382(n).

Example

For n=12, A002182(12) = 240, which is written as "11000" in primorial base (A049345) because 240 = 1*A002110(4) + 1*A002110(3) = 210+30, thus a(12) = 2, as there are two nonzero digits.
For n=18, A002182(18) = 2520 = "110000" in primorial base because 2520 = 1*A002110(5) + 1*A002110(4) = 2310+210, thus a(18) = 2.
For n=26, A002182(26) = 45360 = "1670000" in primorial base because 45360 = 1*A002110(6) + 6*A002110(5) + 7*A002110(4), thus a(26) = 3, as there are three nonzero digits.

Prog

(PARI)
A267263(n) = { my(s=0); forprime(p=2, , if(n%p, s++, if(n==0, return(s))); n\=p); }; \\ From A267263
A324381(n) = A267263(A002182(n));

Crossrefs

Cf. A002100, A002182, A049345, A267263, A324382.

Cf. also A324341.

Sequence in context: A352219 A275656 A228825 * A331383 A201208 A006513

Adjacent sequences: A324378 A324379 A324380 * A324382 A324383 A324384

Keyword

nonn

Author

Antti Karttunen, Feb 26 2019

Status

approved