%I #14 Mar 13 2024 01:50:27

%S 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,

%T 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,

%U 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

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

%H Antti Karttunen, <a href="/A328615/b328615.txt">Table of n, a(n) for n = 0..32768</a>

%H <a href="/index/Pri#primorialbase">Index entries for sequences related to primorial base</a>.

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

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

%e 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.

%t 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 *)

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

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

%K nonn,base

%O 0,17

%A _Antti Karttunen_, Oct 22 2019