A328615 Number of digits larger than 1 in primorial base expansion of n.

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

Offset

0,17

Links

Antti Karttunen, Table of n, a(n) for n = 0..32768

Index entries for sequences related to primorial base.

Formula

a(n) = A267263(n) - A328614(n).

a(n) = A001221(A328572(n)).

Example

In primorial base (A049345), 87 is written as "2411" because 87 = 2*A002110(3) + 4*A002110(2) + 1*A002110(1) + 1*A002110(0) = 2*30 + 4*6 + 1*2 + 1*1. Only the digits 2 and 4 of these are larger than one, thus a(87) = 2.

Mathematica

a[n_] := Module[{k = n, p = 2, s = 0, r}, While[{k, r} = QuotientRemainder[k, p]; k != 0 || r != 0, If[r > 1, s++]; p = NextPrime[p]]; s]; Array[a, 100, 0] (* Amiram Eldar, Mar 13 2024 *)

Prog

(PARI) A328615(n) = { my(s=0, p=2); while(n, s += (1<(n%p)); n = n\p; p = nextprime(1+p)); (s); };

Crossrefs

Cf. A001221, A002110, A049345, A267263, A276086, A328114, A328572, A328614, A328616.

Sequence in context: A337565 A138385 A030614 * A128016 A128017 A096285

Adjacent sequences: A328612 A328613 A328614 * A328616 A328617 A328618

Keyword

nonn,base

Author

Antti Karttunen, Oct 22 2019

Status

approved